Meaning and usage of "bite me"

I often come across the phrase bite me in many TV shows. What does it mean and is there a specific context in which this phrase can be used?

Here is according to Wikipedia:

Bite me is typically used as a US idiomatic expression of discontent or annoyance with another party

According to the Online Slang Dictionary:

a command, similar to "Go to hell!" (i.e. "Leave me alone!" "Go away!" etc.) Note: not considered especially vulgar, but usually considered inappropriate in more formal settings.

Cambridge Online Dictionary tells us how to use it:

used to say to someone that they have made you feel angry or embarrassed

It can also be used as a statement of contempt, or defiance.

I’m afraid this actually is a minced oath, because it’s a cleaned-up version of “eat me”, itself deriving from “suck my dick/cock” — which gives the answer to your question about what body part is being referred to. It also shows why you didn’t find ladies who used the expression.

The Wiki Answers site explains this in rather vivid detail, of which a portion is:

The origin of “bite me” is pretty raunchy. In the late Forties and early Fifties a popular exclamation among teenage boys who wanted to indicate their extreme disapproval with statements or actions made by other teenage boys and sometimes adults, such as teachers, was “suck my dick!” Of course, they never actually said such a thing directly to a teacher. They told their friends that they would like to tell Mr. Jones, the math teacher, to “suck my dick!” But they never actually did so.

Possibly, it was homophobic, since no male in 1950 wanted to be thought of as a “homo”, the then popular term for someone who was gay. If you said “suck my dick” to another male the implication was that your interlocutor was a “homo”. Interestingly, “homo” was usually preceded by the word “little”, as in you “little homo!” So the complete expression was usually: “Suck my dick, you little homo!”

The expression gave rise to two other expressions: “You suck!”; or the ubiquitous “It sucks!”. In the last several years “bite me” has emerged as a cleaned up and shorthand version of “suck my dick!” It has in fact become so sanitized that I've heard talk show hosts on the radio use the expression without feeling their jobs were in jeopardy.

I can confirm that this really is the sense of term from 40 years ago. It somewhat surprises me that people now no longer connect it to its vulgar roots.

Meaning and usage as described by Third Idiot, but I always understood it to be short for bite my crank (that is, for suck my cock) — intended in a demeaning way, but its usage may have softened over time.

Here is an article on the subject that offers some insight. Apparently bite it is the originating term, along with eat it, and, where a location for the snack is specified, it does seem to be in the posterior region, though not exclusively so.

The Urban Dictionary also suggests that it is a minced oath for blow me, but they offer no supporting documentation.

Shakespeare is nowhere to be found.

This phrase was used by the girls (to each other in that vein). When any two girls got into a hot fight it was like saying eat my cunt. Heard it all the time since 1955, but the guys used it much more often. This was in the Chicago area.