'Quai' is equivalent to the word 'quay' in English, meaning a wharf, platform or landing stage built at the side of a body of water. In Paris, roads such as 'Quai St Michel' run alongside the banks of the river Seine. If you have an address with 'Quai' on it, you know that you'll be right next to the river.
By the way, 'quai' - pronounced 'kay' - is also used in French to mean a station platform.