It is a bit complicated.
It does not "confirm" his theory, it only supports it.
Using the matematics that explain the behaviour of space in the presence of gravity (which is the main thing General Relativity does), it was shown that black hole must exist.
IF, for some reason, someone had shown that there is no such thing as black holes, then that would have "unconfirmed" the theory.
As long as nobody could actually "show" us a black hole, there was a possibility that Einstein's theory was false. Once you show an actual black hole, you do not "prove" that the theory is true, you simply remove a possibility of showing that it is false.
Theories are never "proven" to be true, because there can always be a better explanation for what we see. However, it is possible to prove a theory wrong.
In regards to Einstein's General Relativity, this photo shows that, once again, we have failed to prove it wrong.
In science, a theory is a proposed explanation for something that we can not directly check. Every year, thousands of theories are proposed. The job of all scientists is to show why a theory is wrong. In this way more than halp of the theories die withing a year, almost 95% of them die withing 3 years. The theory known as General Relativity has survived for over a century. It has proven to be "useful" in helping us understand how the universe behaves. This shows that the theory (the proposed explanation about how things work) is very close to how things really work. It is possible that, one day, someone will propose an even better theory. However, that new theory would then have to show, for example, that black holes do exist (because we have actually seen one).