Aside from the messaging concerns, there are grown men whipping belts and handcuffs at the camera using audios that describe sexual things, so it's your prerogative as a parent if you want your teen to see those things. The "For You Page" is the screen where you scroll down through all the videos. They start without warning and you aren't sure what the content is going to be.
There's also a lot of cosplayers and makeup artists who do incredibly detailed (impressive really) horror makeup which may affect some more sensitive children/teens. The FYP shows videos of anyone and everyone almost at random, you don't have to be following any of them, so you can't control what you're seeing on the app unless you block creators as their videos come up, but that's futile as there are so many.
It used to be musical.ly, people would just dance to short clips of music and it was fairly harmless. But now there's a bit of content that I would say is inappropriate for children/younger teens but we all have different standards for what is appropriate and what isn't. You don't need an account to scroll down the FYP page, so get the app yourself, have a look at the content and make an informed decision for yourself. There IS a messaging feature, and children have been contacted by groomers on the app before, there are videos and articles about this available with a Google search, so be wary of that.
A lot of the content is intended to be just funny, but humour that older teens who were around for the Vine app era would get. There's many dance videos that are totally innocent and harmless, there are some creators who post fact videos, or videos of them dressing up as people from films such as clueless, coraline, Disney/pixar films, there's someone who dresses up as and makes videos as strawberry shortcake, so a lot of the content is clean, innocent fun, but some TikToks aren't and they do just pop up out of nowhere at times.
If your child has the app and posts videos, anyone can see them unless their account is on private, and some people do save the videos to their phone and put them in a compilation to post on YouTube to mock them, and I'm sure it goes without saying that children and teens need to know that when they post something online it's out there forever, and the things they think are cool or funny when they're younger can come back to embarrass them later, even if it's just a 15 second dancing video.