Anything fishy smells, tastes, or resembles a fish in some way. Suspicious people and situations are also called fishy. Since this word has two meanings, context is key.
If you say something is fishy, it probably means you think something is suspicious. If you’re sitting next to someone eating a tuna sandwich, though, you could just mean you smell a fishy odor. Fishy usually refers to situations that seem suspect or shady. A guy looking over your shoulder while you use an ATM is fishy. A student looking at her arm for answers during a test is fishy. Anything fishy is suspicious — somebody’s up to something.