In the movie Avatar, the Na'Vi have a human-like body; two hands, two legs and a head.
Aside from their blue skin the only overt difference from humans is that they possess a tail.
My question is : Why do Na'Vi people have tails?
The Na'vi have tails for three primary reasons;
The Official Film Companion book states that the Na'vi's tails are used to help them balance their tall forms as well as gripping branches;
"For balancing their long torso and legs, the Na'vi have a long, prehensile lemur-like tail. They can traverse the landscape on the surface as well as using a form of brachiation from branch to branch similar to Earth primates."
This is backed up by an identical reference on the Avatar : Pandorapedia website.
"All Na’vi have a long, prehensile tail. This is used for balance, acting as a moving countermass to smooth out the stride at a full run, and to assist with direction changes. The tail is also used for social cues regarding emotional states, as are the ears. Some Na’vi subspecies can suspend their weight from their tail, but the Na’vi in the Hell’s Gate region cannot. They have been observed however using the prehensile tip of the tail to grip tree limbs and vines during climbing, and to help arrest a fall."
In a pre-release interview, James Cameron discussed the reason that the Na'vi were given tails:
On Avatars having tails, James smiled and said, “The studio asked me the same question. They asked, ‘Do they have to have tails?’ We’re very happy with the way the Na’vi worked out because what we found is the tail and the ears show the characters’ emotional state. A cat owner knows that you can tell a cat’s mood by what its tail is doing. Just as we created a verbal language, we created a vocabulary for the tail and the ears.”
We see Jake and Neytiri interlocking their tails when having sex. It's reasonable to assume that a prehensile tail will contain a sizeable number of nerve-endings so the feeling of two tails pressed together may be sexually pleasurable to the Na'Vi.
In universe: tails are useful to aid balance when running or jumping, that's why Earth animals have them - just look at how a Cheetah uses its tail when hunting down a zig-zagging gazelle.
The Na'vi do a lot of running and jumping in the jungle, and it probably also helps when they ride various creatures. So it's plausible that a tail would confer an evolutionary advantage.
And of course it's a way to make them look more exotic while keeping their shape basically human and thus compatible for the audience to identify with them.
As other's have said, for balance while traversing the jungle is one reason they evolved that way.
I'm surprised to find that no one has mentioned the other function of their tails. Turns out that their tails are extensions of their spinal column and end with a "connector" of sorts allowing them to connect their brain/consciousness with the various animals on the planet and bond with them. So that's another reason for the tail evolution.