The short version is that she used a private, unsecured server on her own property to send and receive tens of thousands of work related emails, a big problem if your work happens to be as secretary of state in the US government. Many of these emails were classified even above top secret level. And they were moving through a computer that anyone with even a basic knowledge of cracking could break into with some scripts that are publicly available for free download on the Internet. Meaning that there is every chance that our enemies/rivals abroad now have those emails, the ones that are so secret that they're higher than Top Secret.
There's also some shadiness regarding why she wanted to do this in the first place, how much of this did she really understand, etc., but those are the basic facts. She, whether intentionally or not, put lives and American intelligence plans at risk by using an unsecured means of communicating about them, a major breach of national security.
Edit: If you're interested in a much longer explanation, complete timeline, etc. complete with quotes and sources, this video goes heavily into depth: https://www.youtube.com/watch?v=yl4RQg4Qfg0&list=PLMNj_r5bccUyulYsatrzNGIvasrOeBy_Y&index=4
Edit 2: Forgot to mention, as to why this is relevant, if you want to be president of the US, commander in chief of the armed forces, and it can be shown that you don't understand basic issues of national security, that's kind of a big problem.
I'll see your 58 minute brainiac Youtube vid and raise you 58 seconds!
Link to video.
National Security has nothing to do with being President.
Hell, Bill lost the nuclear launch codes for a few months and didn't get into any trouble.
It's all about being able to lie convincingly.
Spoiler :