Pressure is primarily when one player or another has a frame advantage. More broadly, it's any situation where both players are subject to some form of recovery and can use the input buffer. When there's an advantage, the player with the advantage is the attacker and the other player the defender.
Pressure can be seen in contrast to neutral. In pressure, how a particular interaction plays out isn't affected by timing, whereas in neutral even a very slow move can beat a jab and a linear move can beat a sidestep. This consistency can, counterintuitively, increase the number of credible options one has to choose from, since by removing this universal risk it makes pokes and movement stronger.
Responding to pressure
In pressure, what options to choose from depends on not just the frame advantage but also the matchup, spacing, wall position, life lead.
More importantly, since Tekken is a real-time game and humans are bad at doing things at random, we can also take into account the opponent's tendencies (i.e. muscle memory) and weaknesses (e.g. difficulty reacting to or punishing certain things) to exploit them.
We should also consider our own weaknesses in deciding how viable certain options are. For example, there's not much point in going for a risky launcher if we can't do the combo for it anyway.
If we have the advantage, our goal is, broadly speaking, to stop movement and challenges with pokes and punish guarding with our strongest mixup. We should also in many cases use movement to more heavily punish challenges.