1) an unspecified period of time, generally used when you wish to impress upon someone that you've been waiting for them much longer than desired.
2) the nebulous "suggested" amount of time recommended before venturing into a place where you have done something immoral, illegal or where something unpleasant has happened.
1) "Shit man I'm sorry, how long have you been here?"
"A good minute"
2) Ya know I'd wait a good minute before I'd go back to the pub, they know you were the one who snaked out on a $100 tab."