A boolean algebra operation on two terms that is true if both terms are true or both terms are false, and false otherwise.

Equivalent expression using basic operations:

(a ∧ b) ∨ (¬a ∧ ¬b)

Truth Table

1 ⇔ 1 = 1
1 ⇔ 0 = 0
0 ⇔ 1 = 0
0 ⇔ 0 = 1

Plain English

Both terms must be equal.

When people say "if" they usually mean logical equivalence instead of logical implication.