In regards to cancer why do cells replicate themselves? If it's a mutation, what kind of mutation would this be classified as?
Hallmarks of Cancer: The Next Generation is by far my favorite article at the moment explaining cancer in-depth. I'd recommend reading through it.
The cells replicate themselves, without regard for normal cellular restriction, due to a number of mutations that accumulate:
So our cancer cells are evading apoptosis. P53 might be knocked down, so cell cycle arrest cant occur, but what about when Akt is constitutively "ON"? Normally P53 can induce apoptosis via the following mechanism:
And as it turns out, Akt inhibits apoptosis in the following manner:
So the cells really aren't dying. What about replicative aging? We find cancer cells have telomerase activity which essentially makes them immortal.
There's also evidence to support regulation of pathways which promote epithelial-mesenchymal transition in tumor cells, and promote invasiveness and cellular motility in most cases:
For the sake of a short response that isn't a wall of text/images, this is a broad survey of some relevant cancer pathways which essentially make cancer what it is. It's more complex than this, but if you put in some research given these hallmarks of cancer, the answers are there.
This article covers some of the key issues of cancer in layman's terms.
Essential, cancer is caused by multiple mutations in key regulatory genes which function in maintaining the cell cycle. This provokes uncontrollably rapid cell division, with only furthers the problem with genetic mutation. Here are some quotes from the article to strengthen your understanding in cancer cell mutations.