As in the title, the reason for the existence of the sequence number is not clear to me.
The sequence number is basically what we call a "nonce": a number used once. When you want to validate a transaction, it is part of the transaction that you sign. Then it is incremented when the transaction got accepted on the blockchain.
This means that two transactions are never the same and by extension always require a different signature. This way, your signatures can't be used to validate the same transaction again and again.