For me infinity is one of the mysteries of the universe. If you ask someone “What is infinity?” it is pretty much the same if you ask this person “What happens after we die?”. So for me the question about infinity is only partially scientific and for the most part is a question of faith.
Personally I dislike the concept of infinity, because it is a very slippery concept. Every time you deal with infinity you also have to deal with all its paradoxes. It is hard to comprehend that infinity minus infinity is still infinity, or that sequence of even numbers is equals to the sequence of both even and odd numbers. It blows my mind, but I still have to deal with infinity, because it exists. I believe so, because if there is no end to count then infinity must exist.
I hope one day humanity will tame this beast called infinity. But for now we have to use the current concept for convenience.
I totally agree that the concept of infinity is difficult to comprehend. For me, that makes it that much harder to work with in terms of math. The concept is complicated enough to deal with in our daily lives!