This site shows you the different types of disruptions and how to get rid of them.
Barrier: Make a match with the Pokemon icon under it or abilities Barrier Bash/Quirky/Quirky+
Unbreakable Block: Ability Block Bash or by making a certain amount of moved
Breakable Block: Make a match with a square next to it or ability Rock Break
Black Cloud: Ability Cloud Clear or by clearing what is underneath