A punish is a term for hitting the opponent when they do something unsafe on block due to negative Frame Data. It can also be used to describe when cutting off false sequences of attacks.
In Street Fighter most characters have negative on Block attacks. The most common negative on hit attacks are reversals such as EX Kazekiri but normal, Unique Attacks, and Special Attacks can all be negative on a individual attack basis. Attacks that are -5 usually can be punish with weak attacks by most of the cast but the higher the negativity on block an attack is the more damage that can be taken due to the mistake.
Some attack sequences do not keep the defending character in Block Stun throughout the whole sequence, using an attack that can interrupt the sequence can also be considered a punish. In most cases not much damage can be done when cutting off due to only lighter attacks being fast enough for the job or 1 hit invincible specials.
Learning to punish optimally is important in Street Fighter games. Not learning to punish attacks can mean opponents can get away with tactics that are unsafe and seem to be undefeatable. Technically speaking any hit for an unsafe attack can be considered a punish. An optimal punish refers to a sequence to hit the opponent and take the highest amount of damage or leave them in a really bad position for tactics such as Resets or prone to being Corpse Pushed while in knockdown. In order to use optimal punishes players should familarize with all the options available to their characters such as their Link, Target Comboes, and game specific mechanics such as Switch Cancel or Crush Counters depending on the game to do maximum damage.
The other punish type is interrupting. This refers to taking advantage of attack sequences that have a gap in blockstun and performing an action that would interrupt the next attack in the sequence. Usually the damage possible isn't high, but this discourages opponents from trying sequences that can lead to chip damage or other otherwise advantational tactics for them.
Whiff Punish Edit
Another subset of punishing is "whiff punishing". This subset of punishing doesn't rely on frame data and usually doesn't even require connection at all of a primary attack. Most attacks in Street Fighter have recovery where after the attack Hitbox appears there is still a brief moment before the player can control their character again regardless of how positive (or negative) the attack is on connection. Most attacks stretch out the Hurtbox even after the attack finishes while the attack is recovering and the opponent can strike the extended hurtbox. Others can require the player to come back into the range of their own attacks (such as the example).