A board on the flop or on the turn is referred to as drawy or draw heavy if it makes a lot of draws possible, i.e. if there are many cards that could complete the draws of the involved players on the upcoming street.
Here's an example of a draw heavy board (also called wet board):
On this board many players could have flush draw, straight draw or gutshot combinations for example. There are many so-called outs that could complete the common draws on this flop on the turn or on the river. The board is therefore draw heavy.
This on the other hand is a very dry board and only offers the player few options to considerably improve his hand on the turn and on the river. It is not drawy.