The "hot seat" is a term commonly used in other sports to describe a person's place on the team. For a starting player they could be in danger of losing their starting gig or a head coach may be close to getting fired.
Most of these situations are the result of years of frustration from fans. In the case of fighters in the UFC, the hot seat can heat up after just one fight. It's a predicament that many of the competitors on Saturday night's show may find themselves in if they don't have a good showing.
In the UFC you must provide production or you can quickly find yourself either on the prelims or even out of the company all together. Although some of these guys aren't likely to fall that hard if they lose, it is a real possibility for others.
Everyone from the main-event fighters to the preliminary competitors needs to bring it or they will start to feel the sweat from sitting in the hot seat.