As a noun: the act of staying awake
long into the night, well beyond the hours one's body is adapted to.
As a
verb: to undertake such an action.
(From sleep deprivation; see also self-deprecation,
depression)
"
Wow, why's Mary look so out of it?"
"Oh, Mary depped all night
studying for her
biology final. Also, she's a crack addict."