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1.
There are at least two usages of "trivial". One is to describe answers, and the other is to describe questions/tasks.

Answers: A trivial answer is something which is either immediately self-evident or which conveys no information.

Questions/Tasks: A trivial question can perhaps be defined as something for which either the answer or the method of finding the answer is known by the person asked the question.
Answers: When asked to describe yourself, a nontrivial answer would be, "My name is Joe Schmoe. I'm 5'10" and weigh 170 lbs." A trivial answer would be, "I'm a human. I know English."

Questions/Tasks: In mathematics, computing the values of integrals is a trivial task, (even though it can be hard), because the methods for computing integrals are known.
by Alexander TG April 29, 2006
 
2.
Someone who acts irresponsibly or with stupidity.
dude1: what the hell/s he doing?
dude2: ahh, what a fecking trivial
dude1: right on
by Carnophage December 15, 2004