Usually occurs sometime in your twenties, a few years out of school and still feel as though you're waiting for you're life to begin.
For most people it will be arround twenty five years of age (give or take a year or two) as this tends to be when you're way of thinking is starting to change beyond that of a high school or college student. Most people realise they've reached this age if they talk to teens online and realise their way of thinking/talking/interacting etc is considerably diffrent and/or they're starting to refer to teens as 'kids'.
It's an age where a lot people start developing a more realistic outlook in life and start feeling that if they haven't accomplished certain things in life they thought they would by then that they may never (Even though this isn't true and they still have a long time to attain their goals and dreams).
This tends to be the age where regets about decitions made in High School, College etc start becomming more appart. The classes one didn't take, or could have tried harder in, the teams one didn't try out for, and wished they had and so forth can sometimes cause a lot of regret and even resentment of those that are doing things one wishes they'd done.
Some people will respond to a quarter life crisis by rushing into various landmark type goals in life (ie, getting married, moving out from your parents house, getting your first house, getting your first real job, having kids).
This could be because their friends have accomplished one or more of these things and they're worried their falling behind them.
It may also be because they're afraid that if they don't accomplish these things by the time their 28 or so, they may never.
Others respond to it by growing depressed and blamming others for their pervieved failures in life.
People tend to move beyond this life crisis when they realise that, a lot of people feel the same way and/or are in the exact same position, so they have plently of company (misery loves company) and/or start to realise that perhaps some of their hopes and dreams were a tad bit unrealistic and that they're just getting a reality check. Once one realises that life hasen't neccessarily let them down and that their hopes and dreams were just that, hopes and dreams, but the reality has simply granted them a more down to Earth/realistic life, they'll accept it and hopefully be happy for what they have and stop lamenting over what they never could realistically have achieved in life.
Person1: What's wrong man?
Person2: Sorry, I'm just kinda depressed. I'm 26 years old yet I feel like I should have been way more then I am by now.
Person1: I hear ya man, welcome to your quarter life crisis.