Post Count is, well, the number of posts a user of an online forum has made. However, many of the Fora out there have developed a mentality that it represents some form of status to have a high post count. They'll downplay people's opinions and make comments about the relative value of members. Obviously, this is fallacious logic (having a high post count only means, well, having a high post count; it doesn't automatically mean that those posts really contributed to anything), but due to the correlation that an active member of a particular forum will have a high post count, it's easy to see how people can make this mistake. This is commonly paired with Suffers Newbies Poorly, as a high post count is frequently seen as an indication that a member has been on the site for a long time, and is thus more "loyal" to the community (without taking into account any actual contributions the member has provided to the forum.)
Somebody who endeavours to raise their post count any way they can is called a Post Whore. Somebody who makes meaningful conversation but also keeps a careful watch on their post count can also be a Wholesome Post Whore, traditionally by boasting about their post count, but it may be less detectable, such as by them checking out the member list for the sole purpose of working out who's the next person they need to beat.
Wholesome Post Whores can actually be pretty productive on a board. The obnoxious kind may just turn into Spammers.
Depending on forum mechanics, it's perfectly possible to have a post count in the negative numbers.