Definition of deepstack
If we dissect the word, we have two words: deep and stack. When you are deepstack, you have a deep carpet, i.e. a voluminous carpet. Since cash games are usually played with 100 big blinds, we will take 100 as a reference. At 20 big blinds and less, you are shortstack. At 50 big blinds, you have a medium stack. At 100 big blinds, you have a classic stack. At say (the number is arbitrary, but it gives you an idea) 175 big blinds and more, you're starting to get deepstacked. At some online poker rooms, you may find cash game tables that offer games at 250 big blinds. There you are really deepstacked!
What's the difference between being deepstacked and being deepstacked?
The more chips you have, the harder it is to play and the more decisions you have to make. When you have a pair of 9 preflop with 5 big blinds, you push all in and it's done. But when you have the same pair of 9s with 250 big blinds, you can't just push all in with your hand. We'll have a lot more decisions to make. The good news is that the more you dominate the competition, you'll want to have a big mat against them. Your advantage over the competition will be more obvious when everyone is deepstacked.