I believe in the existence of Heaven, although I cannot prove it or explain it. The fact that I can conceive of it with a brain that I believe was created by God seems to me to be proof enough. I also believe that there will be a physical aspect to Heaven, although I can't explain that either. I think I've run across a description of it somewhere in the Bible, but I can't recall where.
There is no way to prove whether or not this place exists. However, it is comforting to think that when our loved ones die, they go to a peaceful place where they can still watch over us and be part of our lives. Yet the people you love are never really gone. You keep them with you.
I think if it does exist it is not a physical place. After all, if it is our souls that go there, what is the need of a physical place?
If it does not exist, we say that it does because we want to have hope. Our lives are so precious and so meaningful to us that we do not want to accept that they could end. We want to feel that we can continue to exist forever.
Looking at this question from the point of view of a religious person:
Yes, of course heaven exists. Heaven is the place where God lives, and where He is preparing a place for us when we die. We don't know exactly where heaven is, but it is definitely not thousands of light years away as we imagine it. It is actually really close. For example, Jacob saw in his dream the angels climbing up and down the stairs that led to heaven, and Stephen was able to look into heaven (Acts 7). This shows that heaven is actually closer than we think.
However, not everyone is religious, so from their point of view:
Heaven doesn't exist, because God doesn't exist. However, it is nice for them to be comforted when a loved one dies that they are in heaven, even though they don't really believe in heaven.