A post restriction is a role modifier that restricts what the affected player can post. These range from the objectively quantifiable, such as only being able to post so many times per day, or not being allowed to say a key word; to the subjective, like requiring players to post with a silly accent or so forth.
Subjective post restrictions are usually put into games for laughs; they're a little difficult to judge but as long as the player makes an honest effort to fulfill them there's no problem. On the other hand, objective post restrictions are usually placed into the game to make the game more challenging somehow.
Violating post restrictions can have nasty results depending on the moderator and your role. These punishments range from losing your Night action to getting "warned" to getting modkilled. If warnings are used, it is not advised for them to be given publicly, as that confirms that the player has a post restriction.
Some moderators consider it a modkillable offense to try to coerce another player into breaking their post restriction.
Most people don't like getting post restrictions in general, as they constitute one more thing to hinder their communication, remember when posting, or just get modkilled for when they forget to follow them.
It is strongly recommended that severe post restrictions not be used for balance. Any reasonably clever player can find a way around their post restriction. For instance, suppose you had a Townie who knew who all the Mafia were but could not claim to know this or name the partners inthread. This Townie could instead (fake)claim DayCop and "investigate" every player except the Mafiosi. They're technically within the rules, but still using the full power of their broken role. Of course, the moderator could capriciously modkill someone who toes the line of saying too much, but there's no need to add bad moderation on top of bad setup design.
Games that do not allow roleclaims or nameclaims are similar in this regard.
One trope commonly associated with post-restricted roles is that they also hold stronger-than-average abilities (i.e. a Cop or Vig). However, these sorts of role-post restriction combinations are not actually seen very often in practice.