Imagine that the Earth rotates twice as fast. Now days are only 12 hours long. Years are 730 days long. This wasn't a drastic change or anything, it has always been like this. How would this world be different from our world today? Would humans have developed slower? Maybe faster? The days are shorter, so how would people sleep?
More moderate day/night temperature cycles, possibly milder weather, increased cyclonic weather events, different evolutionary paths for ocean bottom dwellers, maybe mild increases in human technological development, Circadian rhythms would be all over the map.
Let's start by addressing the environmental impacts. From the links above, you'll see that the rotation of the earth is NOT the predominant force driving the atmosphere: convection is predominantly caused by the uneven heating of the surface of the earth, but the directional shifting of the winds is influenced by the Coriolis effect. With faster spinning, the rotation stress would, hypothetical, cause tighter circles of convection. Hypothetically, this would mean boundaries between weather systems would experience more shear stress and, potentially, more cyclones/hurricanes/tornadoes/what have you.
But faster rotation would ALSO mean that there would be less consecutive daylight heating the earth. Consider the following as discussed by Randall Munroe:
When instructions say let stand for 1-2 minutes, it's not just to protect your mouth from hot food—it's giving the hot and cold spots time to equalize, so the whole thing will be sufficiently heated throughout.
Doubling the spin of the earth doesn't alter the total exposure level of the surface, it just changes how frequently the heat is turned on and off:
When you cook something on 50% power, [...] In effect, the microwave is just automating the tedious task of zapping something a bunch of times on "high" for 10 seconds each and letting it sit for a while in between.
Basically, you're setting the earth to "cook" at 50% for 24 hours rather than 100% for 12 - the overall heating experienced is the same, but it's more evenly dispersed. This means that day/night cycles will, on the average, be milder (the difference between noon and midnight temperatures) and that weather events on the whole will probably be LESS extreme.
Now let's talk about the ocean. The last of the links in the top sentence was about the benthic zone. Due to being submerged in fluid, the benthic boundary layer is the area most affected by the earth's rotation. You would see significantly more churning in this layer. This would lead to more rapid dispersal of smaller organisms through the water and the evolution of heavier filter feeders anchored against the sheer stresses (so more water is flowing through their "net" note: these already exist (various corals), but it would be even more prevalent in that ecosystem). Smaller creatures blown by the currents would probably find it harder to reach others of their own species and would likely retain asexual reproduction or parthenogenesis.
Ocean Tides: Tidal rhythms would also be different. Since we assume that the length of the year is roughly the same (doubled in days) and we haven't stipulated a change in the moon's rotation, your spring and neap tides would remain the same, but your diurnal and semi-diurnal tides would be different. Again, a more rapid spin produces a higher Coriolis effect but more even dispersal of force (in this case, gravity). So it's a tossup which of the two will dominate (more frequent high tides vs shallower tides overall). A full mathematical treatment is beyond both the scope of this answer and my current mental capacity.
Now on to humans: With more mild weather patterns (in most areas), we would probably find basic survival easier, plants would be less likely to freeze, fewer major storms (though, as noted, probably frequent minor ones). Human civilization would find things definitely easier, encouraging faster population growth and technological development - fewer people starving in winters, dying in weather and sea storms, etc provides more manpower to tackle problems.
Evolution: With less consecutive daylight and more frequent periods of sunrise/sunset, crepuscular creatures are probably far more prevalent, and possibly dominant. We would probably have evolved larger eyes for seeing in dimmer light, since most basic activities (like farming, harvesting, craft work, etc.) would at least extend into these mixed light periods.
Sleep patterns: Circadian rhythms could be either more rapid (so we'd adjust to shifts in activity cycles faster) or weaker in general, so society would likely adapt to people working off-cycle when they wish rather than everyone (or most everyone) working during the daytime. With artificial lighting, people would liberate themselves from diurnal cycles and rooms specifically created to be "dark" and "light" would be common so people can work on their own sleep cycle without disrupting others.
To this... I'd add that there's a significant effect on winds and the progression of weather patterns that's based upon the Earth's current rate of revolution. Trees, buildings and anything that sticks up from the Earth's surface acts as a brake to the effect of the upper layers of atmosphere that are moving at a relatively high speed. If you were to ascend in a hot air balloon you'd move faster the higher you rose.
In the case where the Earth is now revolving twice as fast then the effects are much more so. Planes could--in theory--take off and land easier without stalling, as long as they were oriented correctly, that is.
Ocean waves would be higher and in many cases would wreck the coasts. Wind-chill factors in colder climates would make most of them inhospitable.
Not sure if I could quantify it but it's entirely possible that we'd have to recalibrate weight scales.
The Earth's shape is somewhat determined by its rate of spin (remembering that it's not solid all the way through). The faster it spins the hotter its inside. The hotter its inside the bigger it bulges around its axis.
If the Earth rotated twice as fast, there would actually be 183 days in a year (not 366/365).
Also, winter would be summer and summer would be winter (they swapped places). And autumn would change with spring so all the seasons would be different!