When someone really wants to do something, they will try hard to convince other people to let them do or not do that thing. They might even be willing to lie or cheat. To describe this, we say that that person will "say anything" to accomplish their goal.
For example, say this about someone who really doesn't want to wash the dishes:
She'll say anything to get out of washing the dishes.
Someone who's truly addicted will say anything to get their fix.
You can also talk about people who will "do anything":
I wouldn't trust him. He's the kind of guy who will do anything to get ahead.