The verbs "mogen … van" (to be allowed, may), "moeten …. van" (to have to) en "niet hoeven … van" (don't have to) are used to indicate if something is done compulsory or permitted.
The word "van" is used to say who has (or hasn't) given the permission (allowing you) to do something, in the example this person would be "mom".
Dat mag je niet |van moeder|.
|Mom say's| you are not allowed to do that.
This sentence can't be literally translated in English. So therefor the word "say" is used (when mom doesn't give her permission, she actually has to say it).
If "van" wasn't used, then you could translate the sentence like this:
Dat mag je niet.
You're not allowed to do that.
I hope this was helpful.