For the consumer usage you will not notice much of a difference. The biggest place that the speed difference will show up is when you are taking many pictures in a short amount of time and then writing them to the card. For example, professional cameras can shoot at upwards of 12 frames per second (in other words 12 pictures in one second). The faster your card is, the longer you will be able to continue shooting at the high rate before you run out of buff space (the small amount of memory your camera stores the images in before writing them to the card.)
You would also see the difference when you are transferring the images onto your computer. With a slow card transferring close to several thousand photos (basically a normal day for a professional photographer in some cases) can take an extremely long time. Faster cards, coupled with faster USB speeds, means less time that you need to wait while your files are transferring.
So basically, the average user wouldn't see much of a difference, however when put to the test of a professional application the speed differences are apparent.