At David Zaslavsky's suggestion I'll transfer this from the comments to the answers (I was a bit hesitant because I don't know how reliable youtube videos are to still be around in, say, 6 months time!):
This little youtube video might help. You can only resolve the objects by looking at the reflected waves. The amount of detail you can get in the reflected waves can't be smaller than the wavelength (roughly speaking).
The video shows incident waves being reflected off small irregularities in the surface at the bottom of the picture. The first case (wavelength smaller than the irregularites) shows information about the irregularities being "fed back" in the reflected waves:
The last case (wavelength larger than the irregularities) shows much coarser information being fed back, making it not possible to get any information about, for example, the size of these irregularities:
Of course snapshots are a bit hard to read, you'd really have to look at the statistics of the received reflected waves as a function of position to really see what was going on, but the video gives a general impression of the problem.