The very basic identifying traits of a Twi'lek are their Lekku (brain-tails, head-tails, tchun-tchin) and multiple vibrant skin colors. They are a very wise and very prominent species. Their females are known to be exceptionally attractive, while the males tend to be seen as ugly, due to their large brow-bumps.
The word "Twi'lek" is actually taken from the Galactic Basic
words "Twin Lekku." Twi'leks also call them "Tchun-Tchin," which is reference to both lekku, as "Tchun" is referring to the left lekku, while "Tchin" refers to the right.
Lekku usually come in a pair, with a second pair very-rarely growing on males from the smaller protrusions in the back of their skull. Males with four lekku are held in high respect.
The lekku serve as storage spaces for sub-concious brain matter, and as such, the skin around them in incredibly sensitive. The lekku are also used to attract the opposite sex, as well as help speak the Twi'lek's native language of "Ryl." Twi'leks can even secretly communicate smaller messages between eachother through the subtle movements of their lekku. Since advancing beyond their home planet of Ryloth, Twi'leks have almost all-together stopped using their Lekku in conversation, as other languages (such as Galactic Basic) have become ingrained in their lives.
Twi'leks have skin colors for almost every color of the rainbow. Funnily enough, the two rarest Twi'lek colors in the galaxy seem to be the most prominent ones in Star Wars video games.
Rutian, or "Water" Twi'leks are considered very rare. They are descendants of Twi'leks who worshiped water, in all its forms. They range from very dark to very light shades of blue.
Tyrian, or "Music" Twi'leks are fairly common, and are descendants of great artists and musicians. Their skin colors range from dark to light purple.
Tukian, or "Spirit" Twi'lek are descendants of shamans and priests. Their skin hues range from light to dark green.
Tolian, or "Fire" Twi'lek are descendants of the Twi'lek who worshiped fire. Their skin is any hue of yellow.
Darian, or "Stone" Twi'lek are descendants of the Twi'lek who follow the Stone Temple Doctrine.
Zhar Lestin, a Lethan Twi'lek
Lethan are essentially the "albinos" of the Twi'lek. These Twi'leks are the rarest of all skin hues. Their reddish or pink skin was actually the result of unique mutations in the Twi'lek's DNA. Many Lethan Twi'leks are sought after by slavers for their rarity, and as such, lead very secluded lives. Despite this apparent rarity, they are among the most common depicted in Star Wars video games.