The phrase "I figured ___" can mean "I thought ___". "Figure" is a more casual word than "think", so it's mostly used in spoken English, rarely in writing. This phrase is especially useful when you're telling people about something that you did, and want to give a little explanation of why you did it:

I figured I'd go ahead and get started on the next set of reports as well.

I figured he wasn't going to show up, so I went ahead and left early.

It's common to explain what you thought by directly quoting your own thoughts like in the example above, and in these examples:

I figured, "Why not make a little extra money on the side?"

I figured, "Hey, let's see how much it would cost to get a new one."