Suspect is something a spell or ability does to a creature, not an ability printed on a card. When a spell or ability tells you to suspect a creature, that creature becomes suspected. A suspected creature has menace, which means it can't be blocked except by two or more creatures, and it can't block at all.
That cuts both ways, and knowing which way you want it is the whole point. Suspect your own creature and you turn it into a better attacker while giving up a blocker — exactly what aggressive black and red decks want. Suspect an opponent's creature and you clear a blocker out of the way, though the menace it gains means that creature can still swing back hard. Either way, suspect pushes combat toward the player who uses it.
