I don't understand what kind of answer you want. Quantum entanglement is a difficult topic. Let's try the same question with gravity:
Everyone talks about [gravity] and there are a lot of fun experiments that imply [gravity]'s existence. But what does really show that [gravity] should exists?
Everyone talks about [gravity] and there are a lot of fun experiments that imply [gravity]'s existence. But what does really show that [gravity] should exists?
Edit: It's very difficult to discuss entaglement without a lot of math, but you can start reading the "concept" section of the Wikipedia article: http://en.wikipedia.org/wiki/Quantum_entanglement#Concept