What exactly is the data in data availability when discussing roll ups in ethereum?

I believe I have a basic understanding of how blockchain works. You have transactions, that get collected into a block and tagged onto each other to form a blockchain.

The blockchain also has a state (current state of things like accounts, balances etc) This current state is as a result of the transactions in the blocks. So for example, if a new block with transactions is to be tagged onto the chain, the transactions it contains would be executed and that would affect the state. Moves it from a pre-state to a post-state (ie updates things like accounts, balances etc)

What I do not get, when things like roll ups are discussed is data availability. What exactly is the data in data availability when discussing roll ups in ethereum? Is this the state?

And I understand, correct me if I am wrong, that one of the scaling strategies is for level 1 (ie the main ethereum chain) to provide data availability so that methods like roll-ups can use it to provide scalability.

Again how does this work? What does data availability has to do with it?