The most popular seems to be "Wurzel" [1] (translated: "root").
The target audience of the magazines are students (pupils) at school, as well as young students at university. The articles explain advanced math topics. Not too advanced, of course, but still far outside what they see in school. The articles use formalisms only where they make things more clear. They build on common school knowledge. Advanced formalisms are only okay if they are introduced in the article. And the articles aren't too long. The goal is that everything can be understood by students, if they are interested.
Also, the magazines usually contain reports about math olympiads and similar activities, usually written by participants (i.e. by students, not teachers).
Finally, these contain math exercises. But don't think of school exercises. Think of math olympiad, just that you have more time to solve them. Students send their solutions in and it is published in the magazine which students solved which exercise successfully.
The latter one should not be underestimated - it is more or less how all these magazines started: You have math competition, the students go back to school, and you want to keep in touch with them, so you offer them so solche math puzzles in their free time, give them feedback to their solutions, and do everything they don't feel alone with their mathematical interests. You can do that individually only with so many students, so you start a magazine for a more efficient communication.