The forested wetland with standing water and cypress trees that provides habitat for alligators is a swamp.
A swamp is a wetland dominated by woody plants, including trees and shrubs, and it may contain permanently or seasonally standing water. Cypress swamps are especially characteristic of the southeastern United States, where bald cypress trees can grow in saturated soils and develop distinctive swollen bases and “knees.”
These wetlands support alligators along with turtles, snakes, wading birds, fish, frogs, and many invertebrates. Slow-moving water, fallen wood, leaf litter, and dense vegetation create shelter and feeding areas. Swamps also store floodwater, trap sediment, cycle nutrients, and hold substantial carbon in wet soils.
The main mix-up is with other wetland types. Marshes are dominated by grasses and reeds, bogs are acidic and fed mainly by precipitation, and fens are groundwater-influenced wetlands. A swamp may be freshwater or, in coastal settings, influenced by tides. Because the clue emphasizes trees and standing water, swamp is the single canonical answer.