What does the phrase "level them up" mean here?

"Level up" is a gaming term meaning to reach the next level, either of the game or the character. Levelling up a character generally brings new or improved abilities. Reaching the next level of a game brings new areas to play in or a greater degree of difficulty.

Yes, the term "level up" means to improve or advance in some way. I'm not sure, but I think the term originates from role-playing games where your avatar starts at level 1 and you do things/quests/challenges to "level up" to level 2 or higher.

References:

Forum post demonstrating real-world natural language use: https://techraptor.net/content/playing-roles-etymology-rpgs

A book using the term in the title (read the book or find your own summary): https://www.wired.com/2011/05/the-secret-origins-of-level-up/

Scroll down to "path of exile": https://www.pcgamer.com/best-rpgs-of-all-time/

Saving the worst for last: https://en.wiktionary.org/wiki/level_up