In fact when you look at a sensor, it's the low pass filter you see, not the sensor surface itself. It's the low pass filter which collects the dust and smears in a digital SLR, and it's the low pass filter you're cleaning when you remove it.
This is a photograph of the Panasonic GF1. What you see through the lens throat is the surface of the low pass filter, and the sensor surface itself is completely covered by it. This camera has a dust removal system which vibrates this low pass filter to remove any dust. The filter prevents the dust reaching the sensor itself. The GF1 isn't a digital SLR, but the principle of the low pass filter is the same on D-SLRs.
This means, incidentally, that sensor cleaning is not necessarily the terrifyingly hazardous process that the camera manual may suggest. You're not cleaning the super-delicate silicon surface of a chip containing millions of microscopic photosites, but an altogether more robust optical filter in front of it. It's still possible to scratch the surface of a low pass filter, of course, especially since they're so hard to get to, but if it's approached carefully sensor cleaning should be quite safe.
Low pass filters are needed because sensors use rectangular arrays of photosites and if you're photographing a subject whose detail includes a fine rectangular mesh of a similar pitch (iron railings in the distance, maybe, or woven fabrics), there's a good chance of interference effects which appear as tiny colour fringes and artefects in the image.
Low pass filters are necessary, then, but they have a side-effect. They work by slightly blurring very fine detail, and this is one of the reasons why digital images always need some kind of sharpening, which usually takes place in the camera and sometimes again when they're being edited on a computer.
This is illustrated by this photograph taken with a Nikon D50. The strength of the low pass filter in the D50 is unusually low, and the result was that this camera's rendition of fine detail exceeded any other 6 megapixel cameras of the time. The bad news was that some subjects would produce interference/moire effects, visible here as diagonal stripes in the railings on the side of the pier.
