The logical operator meaning "if A is true, then B is true". Usually represented with an arrow, something like "A -> B". It is logically equivalent to (NOT A OR B). The contrapositive of an implication is equivalent to the implication.

The truth table for implication:

A  B | A -> B
-----+--------
  0 |   1
0  1 |   1
1  0 |   0
1  1 |   1
Note that the implication is always true when A is false; therefore, you cannot make any statement about B's value when A is not true.