The phrase was brought back into popularity by the feel-good Robin Williams movie Dead Poets Society, but if you think his character was trying to motivate his students to forget about tomorrow and seize the chance to spend the night naked BASE jumping instead of studying, then you missed the point of that film. Like, really missed it.
What It Originally Meant
"I should seize my chance to study for this exam, lest I wind up spending the rest of my life smoking crack in a McDonald's parking lot. Carpe diem!"
"Consider this diem motherfucking carped."
The original, extended form of the phrase is "Carpe diem, quam minimum credula postero," which roughly translates to "Seize the day, trusting as little as possible in the future." Note that it's not about ignoring the future, but rather not trusting that everything is going to fall into place for you someday. It was compared to picking the fruit as it grows on the tree, taking life as it comes and doing the work that's before you.
Of course, that's kind of boring, and so the phrase would probably never have come back into popularity if it weren't for kids thinking it's all about seizing the chance to ramp a motorcycle into your neighbor's pool. YOLO!