What is recursion and how does it make Polygon zkEVM faster? What benefits did the implementation of flonk bring?

Once you have all the batch proofs of a continuous sequence (a chain segment) you can aggregate them. That means that you can for example compute a proof that proves the batch 1 proof and batch 2 proof. You can do the same for batch 3 proofs and batch 4 proofs.

So you can build a tree of proofs where the root proves a full chain segment. You can build this tree with the shape you want and in parallel. You can have one server aggregating proofs 1 and 2 while the other aggregates proofs 3 and 4. This proof takes 10s.

The last step is to send this aggregated proof on-chain. This proof is what stores the rollup state on-chain and allows the user to withdraw the funds. This happens once in a while (30 minutes in the case of the Polygon zkEVM).

For this last step the proof is converted from a STARK to a SNARK (FFLONK), this reduces the gas cost for verifying this proof on-chain. This process takes about 2min and the gas cost of the whole TX is about 350K no matter how long is the proving segment.