Aquatic or marine usually refer to perfumes that contain some aromachemicals that are supposed to replicate the smell of the sea (fresh, watermelon, seaweed, or the like). I usually dislike them because to me they smell too synthetic or even rotten (like rotten seafood). But they are extremely popular in current mainstream perfumery, since apparently most people perceive them just as fresh and clean; moreover, they tend to be very powerful and very long lasting, which is uncommon in fresh smelling perfumes. Many of the perfumes that have references to fresh, water, sport, and the like tend to have marine/aquatic notes.
I'm probably the wrong person to talk about them because I don't like them. I'd say the most common are Eau d'Issey, Aqua di Gio, and the sharpest of them all, Light blue. Earlier examples tend to be more well behaved: New West, Cool Water, and the only one I can stand, Laroche Horizon.
As I mention, for freshness I prefer instead perfumes based on vetiver. Vetiver is a material that smells fresh and vegetal, slightly green and grassy.