Morpho is a peer-to-peer layer built on top of lending pools such as Compound and Aave.
Video introducing Morpho
Morpho works as a lending pool optimizer; it improves the capital efficiency of positions on lending pools by seamlessly matching lenders and borrowers peer-to-peer. As such, Morpho improves your rates while preserving the same liquidity, liquidation guarantees, and risk parameters associated with the underlying protocol.
So, when a user interacts with Morpho-Compound (resp. Morpho-Aave) the same way one would use Compound (resp. Aave), with the same billions of dollars available to be borrowed/withdrawn, and the same collateral factors, oracles, close factors, etc. The only difference for users is that Morpho provides improved rates for borrowers and lenders.
Users of Morpho can receive two rates: in the worst-case scenario, this is the APY of the underlying pool, and when matched, it is an improved rate - this is called the P2P APY. In both cases, users always receive a rate equal to or better than the underlying protocol.
In short, Morpho is the optimized gateway to decentralized lending. Instead of borrowing or lending directly from your favorite lending pool such as Compound or Aave, you would be better off using Morpho-Compound and Morpho-Aave.