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How Does a ‘Light Client’ Utilize the Merkle Root for Verification?

A Light Client (or Simplified Payment Verification, SPV) downloads only the block headers, not the entire block data. To verify if a transaction was included in a block, the Light Client requests a 'Merkle Proof' from a full node.

This proof consists of the transaction and the minimal set of hashes needed to re-calculate the Merkle Root in the block header, confirming its inclusion.

What Is the Difference between the Merkle Root and the Block Hash?
How Does a Block header’S Merkle Root Relate to the Immutability of the Block’s Transaction Data?
What Is Simplified Payment Verification (SPV) and Its Role in Lightweight Wallets?
How Does a Merkle Tree Enable “Simplified Payment Verification” (SPV)?