When you uphold something, you stick up for or support it. Police officers are paid to uphold the law, and crazy Elvis fans uphold their belief that he's still alive out there somewhere.
If you reverse the two parts of this word, you get hold up. And that's exactly what upholding is: holding up or supporting an idea or practice. You might uphold your dog's innocence, even though it's pretty obvious he dug up the neighbor's flower bed. When America fought for independence, we upheld the idea of fair representation. When you uphold something, you're taking a stand for it.