At the bottom left of this thread are two links.
One says "lock topic", and you can click that once you are satisfied that your question has been answered sufficiently. It will keep trolls and spammers (or anyone else) from being able to post in this thread in the future so it won't keep getting bumped to the top of the thread list.
The other says "move topic", and you can click it now to move this topic to the appropriate sub-forum.
Note that those two links are only available to the person that creates the thread (and the forum moderators).
Here's a link:
https://en.wikipedia.org/wiki/Digital_signature
You'll see there that "A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or documents".
In the case of a bitcoin transaction, the transaction itself is the "digital message" that being demonstrated as authentic.
The digital signature doesn't "confirm the ownership of the private key". What it does is prove that the message (or in this case the transaction) was signed by a person in possession of the private key.