How does entanglement become a usable resource in quantum information processing?

[Dennis.B]

I'm a physics undergraduate trying to wrap my head around the practical implications of quantum entanglement beyond the classic "spooky action at a distance" description. While I grasp the basic mathematical formalism from my coursework, I'm struggling to conceptualize how the loss of individual particle identity in an entangled state actually translates into applications like quantum computing or cryptography. For those with more expertise, can you explain in relatively plain terms how entanglement creates a resource for quantum information processing that isn't possible with classical correlations? I'm particularly confused about how measuring one particle instantly determines the state of another, and what that really means for transmitting information or performing a calculation.