The suicide grip is a hand position on a barbell or dumbbell. The thumb is not wrapped around the bar while using this grip. Often people who feel very confident lifting a certain weight will be tempted to use this grip. The problem with this hand position is that the bar can easily slip out of your hand.
In 2009 a University of Southern California running back named Stafon Johnson made the news when a 275 pound barbell slipped out of his hands and landed on his throat. He was using a suicide grip at the time because he was probably very confident lifting that amount of weight.
This grip should be used with great caution, or avoided completely if it is possible. It is dangerous, especially if you are lifting alone. You should at least wrap your thumbs around the bar. The safest and most secure grip is the hook grip.