Definition of reg
A "reg" is a shortened way of saying "a regular". We're talking about a regular poker player, one that we see on our tables every day. A regular is not only a regular player, but also a winning player. If a player is present at your tables every day, but loses day after day, he is not a regular, but a "fish" or "reg fish". When playing against a reg, we assume that he is decent, that he knows how to play and we try to limit our interactions with him. A reg is a winning player who studies his game and is serious about his game.
What approach against regs?
When you are at the poker table, you want to identify the regs and the fishes. You want to take as many notes as possible on each one. Obviously, you'll want to play as many hands as possible against the fishes and as few hands as possible against the regs. To better deal with regs, it helps to know them well. Always have your notes on them in mind and play according to the information you have on them.