I'm looking for a way to disable the ability to approve edits for certain users. That means they should still be able to write and edit articles, but they shouldn't be able to approve them making them visible to the public.
Is there a way that each edit has to be approved by an administrator / someone with higher privileges?
You want to look into "advanced permissions":
http://www.concrete5.org/documentation/general-topics/simple-permissions#advanced