If you're not familiar with the Madness series, you may want to watch the other installments before this one, just so you'll have some idea of what's going on. (The earlier ones are sillier, and the art style's more primitive, but they're still very enjoyable.) The recommended order of watching them is, unsurprisingly, 1, 2, 3, 4, 5, 5.5, 6, 6.5, 7, 7.5, 8, 9, 10 and 11. (There's other side animations that aren't essential to the ongoing story.)
If you want to learn more about Madness in general, there's a wiki, and Newgrounds has collection.
If you don't like ultra-violent cartoon killings, this is NOT for you.