If a teacher watches you suspiciously while you take an exam, she's eyeing you with distrust or wariness — she might think you're stealing glances at your friend's test paper.
This adverb has two meanings: "with suspicion" and "in a way that arouses suspicion." So that distrustful teacher might glare at you suspiciously, but you can also behave suspiciously, craning your neck to look around the room and gesturing to your friends. If you don't want someone to look at you suspiciously, don't act suspiciously.