"The cat is between the bed and the table."
Translation:Кот находится между кроватью и столом.
You already know there's a cat, you just don't know where. That's why the cat coney first and the New information comes afterwards.
You're sentence would be translated as "there's A cat between the bed and the table" (here, the cat is the New information).
Compare with the explications at "перед мальчиком словарь" and "словарь под тобой".
"Есть" emphasizes the existense of the cat. I can suggest the situation when this can be used:
I think there is a mouse in this house, so we need a cat to catch this one. Did somebody see any cat here?
Yes! I know that кошка есть между кроватью и столом, it has its pillow for sleeping there.
So bring the cat here, please.