The idea: Diffie-Hellman with curve points: one node sends aG, the other sends bG, and each multiplies what it received by its own secret to reach the same point abG, which becomes the key for an encrypted link. The bet is that someone watching aG and bG can't reach abG.
Why it matters: Protects the encrypted connections between Ethereum nodes.
Agreeing on a secret in public
Alice and Bob start from a public color, each mixes in a secret one, and they swap the mixtures in the open. Each then adds their own secret color to what they received, and both end up with the same paint. An eavesdropper has seen both mixtures but can't unmix them. In the real protocol, mixing is multiplying a curve point by a secret number.
The details
On the map: on the curve
Given a·G and b·G, compute ab·G. If discrete log is easy, this is easy too.
It is what makes elliptic-curve Diffie-Hellman key exchange secure[1], which Ethereum nodes use to set up encrypted peer-to-peer connections (KE)[2].