Birds and Reptiles usually develop colorful displays for mating purposes. The general concept is that the colors denote exceptional health of the individual (usually the male). In some cases, like the Peacock, the display actually suits no functional evolution purpose other than showing off to the female that, in addition to being suited to live in it's environment, it can do so to egregious success. One thing to note is that in this evolution paradigm, it's usually the gender that is typically supposed to court the discerning other gender that is the more colorful member of the species (Compare the always male "Peacock" to the drabber always female "peahen" which is usually shades of brown. The gender neutral term for the species is "Peafowl", FYI). So your aliens would likely see vibrant color displays a sexy and attractive.
Other elements are more enviornmental. Tigers, Cheetahs, Leapards, are considered quite colorful for wholly different reasons, namely, camouflage. Humans actually have very developed eyesight that mixes both trichromatic vision (our eyes are simulated by three colors, but all colors we are capable of seeing are combinations of various levels of those colors. It's like how computers use the RGB values to display color... only humans have a wider range of color discernation than computers are capable of producing.). There are some animals with four color vision (turtles) and some with better range (raptors (birds of prey, not dinosaurs... well... Jurrassic Park Dinosaurs...) can see up to two miles away, but have terrible short range vision.) and other animals have low levels of light of nocturnal vision.
I say this, because much of hominid development was focused on becoming apex predators, and members of the Homo genus are uniquely the only predators that are ranged hunters on planet earth, which requires a rather unorthodox set of evolutionary developments to accomplish. Bipedalism was thought to be a means of attaining better height for vantages, our arms are developed for throwing (Our nearest evolutionary cousins throw at 1/5th our ability)... and of course our vision was developed to better assess the lay of the land and see things we should be, which is why we don't think of the tiger and zebra as all that hidden... because it counts on tricking animals with less developed sight... Even intelligence is thought to be a result of developing towards this hunting niche, take a look at the physics of throwing a thing, and remember the best hominids relied on understanding that skill.
Other colors in the wild are based on consuming biological componants that the body cannot break down or dispose of easily. Flamingos, for example, eat shrimp almost exclusively and the material that makes shrimp pink isn't digested or excreted, so they grow pink overtime. There are conditions where humans can have this happen too. The biological compound known as Beta Carotine is responsible for a lot of fruits and vegitables we eat that have a red color. The protein isn't synthisized in animals, but does play some roles, even in humans. For example, it's used to make menolin, which blocks UV rays from damaging skin cells in humans... and if consumed in excess, humans can have an almost "orange" appearance, both in skin color and hair color, since it's usually digested for use in skin pigmentation, and not excreted in bulkier waste products (It typically will leave the body through dead skin).