Yes it's the polite past tense of わかる, and I think you're right with your translation. The most polite way to say "I understood" would be わかりました but you can use わかります if you want to sympathize with someone like you have a mutual understanding of something. Like your friend is like "学校は大変ですよね”　”そのことわかります”. And if you want to use it to express annoyance like "okay I got that, don't treat me like an idiot" you use ”わかっている”. I would use the plain form if I wanted to say something equivalent to "alright, okay, I get it" わかった or わかる.