Don't know this electrical part, what is it?

Wow, the first thing you want to do is attempt to find some Corrosion X and spray all that rust with it. That alone will save you future headaches. From that picture I'm guessing that rig sat out by the Texas Gulf coast for awhile.

There isn't enough to see in your picture, but I think it's a good guess that it's the emergency start off the house batteries relay. That is a pretty stout wire going to it and it would carry a lot of current.