The PS4 ships with a reasonably-sized 500GB hard drive, but it's quite lackluster in terms of speed. The drive only spins at 5400 RPM, but it can be easily upgraded to a better drive -- say, a 7200 ...
Straight off the bat the biggest improvement that you’ll get by stuffing an SSD into your PS4 is improved loading times. Simply put, just about every game you own will load much faster from an SSD.