Telepathy is defined as "Transfer of information on thoughts or feelings between individuals by means other than the five classical senses". That leaves some form of communication not detectable by human senses, though not necessarily some form of communication not detectable by human technology. The question also specifies evolution of such an ability, so this would imply that it is of biological, not technological origin.
Since such tropes as "psionic radiation" or "mental waves" that can be transmitted from one human to another have been not been shown to be anything more than fairy tales by science, we cannot presuppose that they exist for another species.
However, this leaves quite a large range of possibilities for communication that is not detectable by human senses. The electromagnetic spectrum covers a wide range of frequencies, most of which (with the notable exception of the visual spectrum) is not detectable by human senses. Detectable by human instruments, perhaps (I'll discuss that "perhaps" later), but detection by human instruments isn't the definition. There is also the possibility of sonic communication using frequencies not audible to humans, manipulation of magnetic fields, and emission of pheromones not detectable by human olfaction. So, there are possibilities for "undetectable" communication.
Process of Elimination
If a species is to communicate memories, thoughts and sensory data at a rate that allows them to think and make decisions in a corporate manner, then whatever form of communication they use is going to require a very high bandwidth. This means that whatever form of communication they use is going to have to be high frequency, as studies in data transmission have shown that the higher the frequency of the carrier, the more data it is able to encode per unit time. This then immediately eliminates pheromones (which are inherently slow) and low frequency sound. There are still a lot of possibilities remaining.
Another characteristic of Telepathy is that it is long ranged. When we consider sonic communication, we find that low frequency sounds travel much further than high frequencies, however we have ruled out low frequency sound as having too low a bandwidth, so this effectively rules out sound almost entirely. When we examine the electromagnetic spectrum, we find that the highest frequencies (above the ultraviolet end of the visible spectrum) are blocked by an atmosphere similar to our own (but they may not be in another atmosphere), as is most of the infrared part of the spectrum, and some (but by no means all) of the frequencies in the infrared and microwave parts of the spectrum. Lower frequency microwaves and higher frequency radio waves are long-ranged in a terrestrial-type atmosphere, though long-wave radio is not.
So, the best candidate for high speed data transmission is microwave radiation. This leaves the question of how a life-form might go about generating such radiation. The following is educated speculation.
The highest likelihood for "telepathy" is in a species that is able to precipitate a variety of metals in a variety of forms. (This also requires an environment high in metals.) If such a species was using metal to enhance its neural transmission rates (electrical transmission is vastly faster than human nerves' sodium-gate depolarization system), which is in itself a highly advantageous strategy in evolutionary terms, it is likely that creatures using metal as a nerve conduction rate booster would have found that unshielded nerves would cause radiation detectable not only within a creature's own body, but in other creatures too. As faster nerve conduction is too great an advantage to give up, shielding would have evolved, most likely by running nerves through the centers of metal bones. However, the possibilities of transmission and detection of EM radiation means that not all metal nerves would have evolved to be completely shielded, some could be partially shielded and be used to detect EM radiation, while with higher voltages (as demonstrated by the electric eel), other neuron-evolved organs could generate EM radiation of reasonable power.
We then get to the point of bandwidth. EM radiation emission may well have begun at lower radio frequencies, but it is entirely possible that mechanisms could have evolved to increase the frequency of emitted radiation. Since a system of this type could have practically each neuron driving an EM transmitter of a different frequency, high bandwidth can be achieved by rapid changes in signal amplitude and frequency that is allowed by using high-frequency EM radiation, and also by multiplexing - using many frequencies simultaneously. This could allow an evolved bandwidth many times greater than our own Wi-Fi communication, which would also be somewhat directional. Another argument for higher radio frequencies and microwaves is that smaller antennas are required.
Since all this bandwidth is relatively easily achieved in evolutionary terms - simply by duplicating the relevant organs - there is no reason why the beings would not evolve to make use of this bandwidth. Since the highest intelligences of species on earth are found in those creatures with an active social life (and this ability makes for a great social life), the evolution of intelligence is pretty much a given.
If we consider the data bandwidth of the human voice (not the bitrate required to duplicate the sounds accurately, but the actual volume of data it conveys), humans may be able to achieve a data rate of perhaps a few hundred bytes per second at most, including the emotional sideband on top of the raw data. Our hypothetical telepathic aliens could achieve a data bandwidth in the order of tens to hundreds of megabytes per second.
Our telepathic aliens would need very fast brains to process all of this data, but fortunately since they incorporate metal in their neural structures, this is somewhat easier to achieve. The main bottleneck would be chemical neurotransmitters - if they used them. Fortunately, there are other possibilities for cell-to-cell communication. One possibility is an electrical connection, the other is a mechanical connection. Either of these are equally possible, and neither provides particular advantages over the other.
Given all this data bandwidth and a brain capable of processing it, it is entirely possible that each of these beings could communicate highly detailed messages - certainly including thoughts, memories, queries and answers - with a number of its fellows. Considering that much of their brains would be involved in running and interpreting the "telepathic" communication, they may not have all that much capacity remaining for actual original thought, so on an individual basis they may not be much more intelligent than a human, quite possibly somewhat less so, however they do not really need to be any more intelligent on an individual basis given that when they have a problem that they need to solve and cannot do so on their own in a reasonable time, all they have to do is ask a few friends and share the load of considering all the options. Considering the range of microwave communication, these friends need not even be within visible range, they could be hundreds of kilometers away.
Sharing of memories would happen almost automatically as individuals added them as context to the problems they are asking for help with, and the advantage of shared experiences cannot be underestimated.
As for detectability by human technology, an evolved pattern of communication over multiplexed amplitude and frequency modulated radio and microwave bands could certainly be detected, but it would most likely be fantastically difficult to interpret, and to the uneducated and unsuspecting observer (who is most likely detecting "interference" on only one frequency at a time) would find it hard to distinguish from noise. Anyone ever actually listened to a 56k modem on their phone line? It sounds a lot like static. It would require extensive computer support and years of work to even begin to interpret communication like this.
Since higher frequency microwaves (that can carry more data) are attenuated by the atmosphere more than lower frequency emissions, these beings would be able to communicate faster with nearer compatriots than more distant ones, and this would give them the tendency to form regionally-restricted social groups rather than a single global society.
As to what these beings may look like, I imagine them with mobile structures that would look a little like short, thick tentacles that house the microwave transmitters and receivers. They would also be very likely to have inhumanly fast reaction times given the speed of their nerves that is necessary for their mode of communication. They would most likely be able to see some frequency of visible light and be able to hear, but the limits of their vocal communication - if they were capable of that at all - may be some sort of sound that communicates little more than a threat, warning or submission to other species that do not share their mode of communication. I leave the rest to your imaginations.