Final Cut Pro X
It makes editing easy and quick. Basically, putting all of the individual photos into a video, and adding sound effects, music and text. I made a video on how I edit in this software on my second channel. Similar Software: Adobe Premiere Pro, Sony Vegas Pro.
Adobe Production Premium
Used for all video effects that FCP can't handle. Including explosions, floating objects, blood. I used a lot of this software in Box of Color. See the 'Making Of' video to get an overview of how I do effects in it.
Used for editing photos and individual frames. I mainly use it to remove the backrounds of objects, which is really simple.
Used for making graphics (mainly for games and this website). But I do make some for my videos.
Action Essentials 2
Not actually software, but an effects package. It comes with a lot of stock footage, such as explosions, blood, dust etc. I've used it in every animation since I got it.