Marshy things are squishy, wet, and soft, like a marsh or a bog. After three days of rain, your backyard just might be too marshy to set up the volleyball net.
Any area of ground that's waterlogged is marshy, like the marshy shore of a river or the low-lying marshy patch in the neighborhood dog park. Unless there's a drought, swamps and bogs and wetlands are always marshy, and water-loving plants grow happily in these areas. This adjective comes from marsh, which has a Germanic root, mari, that means "sea."