What is the entanglement in quantum physics exactly?

It’s probably going to be hard to find a website that won’t overwhelm you with math ...

In a nutshell, suppose you had two spin 1/2 particles created thru some process from a spin 0 particle. Spin is a kind of quantum angular momentum that is conserved. So, if you create two spin 1/2 particles from a spin 0 particle, the two spin 1/2 particles must have opposite spins. If one is spin + 1/2 and the other has to be spin -1/2.

The spin of either particle is an indefinite state - it  is a quantum superposition of both 1/2 and -1/2 so It remains indefinite until you measure one of the particles. You essentially force it to assume one or the other state when you measure it. If you then measure it to be 1/2, the other particles spin will HAVE be measured at -1/2. And, the other particle could be a light year away.

It has been shown by experiment that the combined quantum spin state of the two particles is entangled - no matter how far apart, the two particles assume the proper opposite state when one of them is measured.