Wiper blades are like squeegees.
The arms of the wiper drag a thin rubber strip across the windshield to clear away the water. When the blade is new, the rubber is clean and has no nicks or cracks. It wipes the water away without leaving streaks. When the wiper blades age, nicks or cracks form, road grime builds up on the edge and it doesn't make as tight a seal against the window, so it leaves streaks. Sometimes you can get a little extra life out of your wiper blade by wiping the edge of the blades with a cloth soaked in window cleaner until no more dirt comes off the blades.