I have Bitcoin Core wallet.
I wanted to know if each transaction I need sync the wallet?
(I have a new business that accept bitcoin and I must to save each transaction)
With Bitcoin Core you'll run a full node. So, for every transaction someone does to your business, your Bitcoin Core wallet need to be synchronized with the complete blockchain.
When you create a transaction, the transaction is broadcast to other Bitcoin nodes and reaches miners.
When a miner includes your transaction in a block that they successfully mine, they broadcast the block that contains your transaction - this is the first confirmation. When other blocks get mined on top of that block, those are additional confirmations of your transaction.
When you run Bitcoin core on your PC it will try to synchronise your local copy of the blockchain. It needs to get the latest blocks to add to your local copy of the blockchain so that it can find out whether your transaction got confirmed.