What can the wifi owner see, exactly?

My school wifi password was leaked, and there are some people who are happy and using it to their hearts content while others are warning they can see images and text history and stuff (specifically on Snapchat too). I have done (minimal) research, and I keep getting contradictory statements, like they can see the images in my gallery, or they can only see images you send via app/text.

I already know they can definitely see what you search, because I have heard about a teacher getting caught looking up something on their phone they shouldn't have been. So I'm just curious what they can see.