The closer to the mid-point of the string (i.e. the twelfth fret) that you strum, the fuller the sound will be. This is because the string vibrates more evenly.
If you were to divide the strings into quarters, then video yourself strumming about 1/4 up from the bridge, then watch the thing in really slow motion, you'd note the the bottom and top quarter vibrate together, and the the middle half vibrates on its own. (This is a poor paraphrasing of something Dave Means pointed out elsewhere, but I hope it's reasonably clear.)
This produces different overtones (secondary tones???) than strumming midway along the scale length.
Not to say that even strumming smack up against the dang bridge is wrong, per se. If you're looking for the plinkier sound, that's where you'll find it.
It's simply that the physics of the strings will produce fuller sounding notes, especially on a short-scale instrument like the uke, if you strum about midway on the strings.