How a transaction proves its ownership of the its source, which can be one or multiple unspent output?

How a transaction proves its ownership of the its source, which can be one or multiple unspent output?

I read the following from the book << Mastering Bitcoin >>

"As you may notice, the transaction contains an empty scriptSig because we haven’t signed it yet. Without a signature, this transaction is meaningless, we haven’t yet proven that we own the address from which the unspent output is sourced."

I am wondering how a signature can prove that this transaction owns the address from which the unspent output is sourced?

https://ift.tt/2r4Ni7x