An implication is something that is suggested, or happens, indirectly. When you left the gate open and the dog escaped, you were guilty by implication.
Implication has many different senses: Usually used in the plural, implications are effects or consequences that may happen in the future. You might ask, "What are the implications of our decision?" Implication is also the state of being implicated, or connected to something bad: "Are you surprised by their implication that you were involved in the crime?"