A sealed envelope for a number: you can't change what's inside later, and nobody can peek.
The idea: Commit to a number v as v·G + r·H, using a fresh random r and two points G and H whose relationship nobody knows. The random r blinds v completely: every possible v fits the commitment with some r. But opening it as a different value would require knowing how H relates to G, a discrete log. And commitments add up: the sum of two commitments commits to the sum of the values, which lets a blockchain check that inputs equal outputs without seeing any amounts.
Why it matters: Used in private transactions and zero-knowledge proofs.
On the map: binding only (hiding is unconditional)
A commitment is a sealed envelope: you fix a value now and reveal it later. Pedersen commits to v as g^v × h^r[1].
Hiding is unconditional: every value is equally consistent with the commitment. Binding relies on discrete log: opening to two different values would reveal the log of h. Commitments can be added together, which confidential transactions (Monero, Mimblewimble)[2, 3] and many zero-knowledge proofs use.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.