In quizbowl parlance, the Big Three are the categories of literature, science, and history. The Big Three are so named because they each take up a comparatively large share of the distribution (and take up a majority of most packets when taken together), and are therefore viewed as particularly important categories to the game.
In ACF and ACF-style tournaments, the Big Three each take up at least 4/4 tossups/bonuses out of a 20/20 packet (so each one takes up about 20 percent of the questions in a packet) and together they make up 60% of any given packet. The amount of any individual Big Three category is almost never reduced or increased from 4/4 without changing the other two as well, because of the imbalances that would result for players specializing in the reduced category (and the complaints that would result over the potential for skewed results and the like). NAQT's percentages are similar, though there isn't perfect parity (NAQT packets feature slightly more science than literature or history) and they can vary slightly from packet to packet.