Not all kayak paddle blades are feathered, actually. The term feathering refers to the act of having the two blades at different angles from the horizontal line. When the blades are not feathered, the paddle can easily lay on the ground flat. When the blades are feathered, they are turned at angles to the horizontal, usually thirty, sixty or ninety degrees off the horizontal line.
The purpose of feathering is to help you keep control of your paddle during times when you’re traveling into higher winds. The higher angle- say sixty degrees- will allow you to cut through the high winds more easily and slice down into the water with each stroke. Conversely, if the winds are at your back, the tilted blades act something like mini sails, allowing you to harness the wind to help you power into the next stroke.