"...I don't know what that means either. After the process???..."

Sort of. Processual archaeology was, roughly speaking, the "New Archaeology" of Binford and others, which concentrated on materialistic explanations for how societies operated. Very useful, but it tended to marginalize or totally ignore other reasons why people and societies do things, involving ideology, perceptions and worldview. Post-processualism developed in reaction to what was seen as an overly mechanistic approach - actually, as an attempt to put a more human and less potsherdy face on the past. At their extremes, both approaches can lead to some very silly stuff. Used as complementary approaches, they can be pretty powerful. In practice, I'd say most archaeologists use theory from both sides of that P/PP divide, and very productively.

A fable to illustrate the two extremes:

A processualist and a post-processualist, walking together down a country lane, come upon three blind men examining an elephant.

The first blind man, who is holding the trunk, says, "Clearly, an elephant is very like a snake." The second blind man, running his hands over the elephant's side, says, "I think not. An elephant is much more like a wall." The third blind man, who has captured the elephant's tail, says, "You're both insane; an elephant is obviously like a rope."

The processualist shakes his head, and says, "Nothing these men say is valid. What we have here is a large-bodied quadruped with a prehensile proboscis."

The post-processualist shakes HIS head, and says, "Only what these men say is valid. What we have here is a snake, a wall, and a rope."