What is this screen called and how do I edit the notifications displayed on it?

[rob damiani]

What is this screen called and how do I edit the notifications displayed on it?

 

[JoeMcJoe]

Does your phone display that AT&T when you connected to a AT&T supplied microsell in your home?

Do you want to stop individual applications posting notifications 100% or partially?
Looks like you are using a thirdparty settings selection tool app too.