How Pedersen Commitments Work
In Monero, Pedersen Commitments are a core component to hide transaction amounts while still allowing for cryptographic verification that no coins are created or destroyed in a transaction.
A Pedersen Commitment to a value v (the amount) with a random blinding factor r is:
C = v ⋅ H + r ⋅ G
C: The commitment
G, H: Generator points on the elliptic curve (with H unrelated to G)
v: The amount (hidden)
r: A random blinding factor (also hidden)
This commitment is:
Hiding: You can’t determine v from C without knowing r
Binding: You can't change v later without altering the commitment 
