"Big bet" is really a fixed limit poker term, and I don't think there's a standard abbreviation for it. In LHE and LOH it's referring to a bet on 4th or 5th street, where the bet size doubles compared to PF and 3rd street (which would be a small bet, so: two small bets = one big bet). This same concept also applies to Stud games, although with some variation depending on the exact game and certain circumstances.
Anyway, in limit poker it's fairly common to calculate the pot in terms of big bets to figure out whether or not a call might be profitable; basically it's (implied) pot odds
, but adjusted for the nature of a limit game. I have also occasionally seen this term used in texts referring to NL/PL games, but, as dj correctly pointed out below, it's not a clearly defined term in that context and thus usually requires further explanation as to the author's intent.