When your contract is ready to be signed, choosing the Finalize & Request Signatures option will result in two things happening:
An email with a link to sign the contract will be sent to you and your clients. You can sign the contract by clicking on the link found in the email you receive.
The contract will no longer be editable. Instead of being brought to the Edit screen when you click on a finalized contract, clicking on the finalized contract will allow you to view and sign it.
Optional Auto-Sign
Another option is you can automatically sign your contracts by following the steps outlined in this tutorial. Your signature will automatically be added after your client(s) have fully signed the contract.