Definition of drawing dead
When we say in poker that we are drawing dead, it means that our equity is at 0. When you're drawing dead, it means you're all-in with a draw, but even if you hit your draw, you still won't have the best hand. Being drawing dead can happen to any player, but generally speaking, good poker players will avoid these situations as much as possible. If you're frequently drawing dead, it's probably a sign that you need to review your game.
An example of a drawing dead hand
You are on the small blind with AK in the heart. The players lie down until the button that opens. You raise and your opponent calls your 3bet with a pair of 8's. The flop comes 872 with a heart color draw (your draw). You bet and he calls the bet. The turn is a 2 which makes a double on the board. You go all in on the turn and your opponent flips his pair of 8's. Here you have 0% equity. Even if you hit your flush, your opponent will still win the hand.