Every level reduces the amount water slows the player by ⅓, including reducing the speed at which flowing water pushes the player when standing still. An armor stand carrying armor enchanted with Depth Strider also moves more slowly when being pushed by water.
Level 3 lets the player swim as fast as walking on land. Any higher level has no effect on speed. Also at level 3, a speed potion affects the player's swimming the same as walking.