A slang term used by a group of teenagers, representing the process of intercourse. The "P" representing "pussy" another slang term for the vagina. P-time simply means the act of a man(or in odd situations a woman whom happens to have a penis) placing their penis in the vagina, for the age old act of sexual intercourse.

When you eat dirt for the first time and leave your family to build a shack in the woods

This is what happens after a Teaching Assistant has decided it just doesn't matter anymore. At this point he or she makes his or her way to the board, exclaims "It's Pee Time" and just unloads.