A stack is deep if it is substantially larger than the maximum table buy-in. If a player has 200 dollars at a table where the maximum buy-in is 100 dollars, his stack is deep. Such a player can win money from other deep stacks, but is also vulnerable to losing a lot of money at once.
This situation has an impact on the style of play and strategy, since a player with a deep stack can get better implied odds and can undertake cost-intensive moves. The cost-benefit ratio, based on the idea of pot odds and implied odds, is shifted because the costs may be higher in relation to the possible winnings.
In a tournament, a stack is deep if it is large in comparison to the other stacks at the table and to the forced bets.