The post count is a measure of how many posts a certain user has made.
Spamming to increase post count Edit
It is not uncommon for competitive users to spam to increase their post count, often deleting posts to erase the evidence that they have spammed (deleting posts doesn't decrease your post count number). This sometimes takes place in the form of playing Post in a Row or Post and Combo to Score excessively, which isn't technically spam, but is posting extremely quickly to up their post count.
Post count related games have popped up every now and then. One of the more recent ones was located here, and was a competitive race, although in the back of the TBG section, you can find many "Who can post last before I reach X posts" topics.