Hydra is a genus of cnidarians, or aquatic animals, that look a bit like sea anemones that went on a heavy diet. They can be harmful to fish fry and small organisms like baby shrimp and snails in an aquarium, and are a nuisance as even adult fish get irritated when brushing against their stinging tentacles. Hydra are often introduced into the aquarium hitchhiking on plants or driftwood.
They're whitish and a bit hard to see, but are definitely visible. Look for a thin sea-anemone-like thing on your plants, glass, heater, or any surface. I'm guessing that an average hydra (the one in aquariums) is 1/5-1/4 of an inch high.