Try fitting a hundred people in a space meant for fifty. They may all fit, but everyone would be very uncomfortable, won't they? Similarly, when too many pixels get packed into a sensor the size of a fingernail, the pixels aren't able to capture light optimally. Of course, when the light is aplenty and the sensor sensitivity is low (ISO 400 or less), one might get great images. But once we hit the 'low light' stage of the day and the sensitivity needs to be bumped up in order to capture a photo, we end up with a 'hot mess' of red and blue pixels.
The reason for this is that the conventional sensor in point-and-shoot cameras is of a fixed size (with an area of just a little over 1 cm) and there are only so many megapixels one can pack into that area without compromising image quality. The tradeoff in the megapixel war is between detail and quality. At the lower end of the spectrum, you get great image quality but not enough detail. As you crank up the megapixels, the level of detail captured goes up, but the image quality goes down. The optimal resolution range for a point-and-shoot sized sensor lies between 9 and 14 megapixels.
More megapixels mean better detail in images, larger prints, and also gives you greater control over image quality when you crop it. However, camera manufacturers realize that in order to by-pass the limitation imposed by the current sensors, only one of two things could solve the problem - either an increase in sensor size (something that would drastically increase the cost of cameras) or redesigning the sensor altogether in order to make it more efficient.
Since a larger sensor meant venturing into DSLR territory, manufacturers felt it best to work on the current sensor design. To this end, Sony created their first 'backside illuminated sensor'. A conventional sensor is designed like the human eye, with the lens in front, followed by a wire matrix and the photodiodes at the back. This design causes some of the light hitting the sensor to reflect off the surface, allowing lesser light to hit the photosite (light collecting pixels on the sensor). The backside illuminated sensor handles this problem by placing the photosite above the wiring matrix, eliminating the reflections caused by the same and therefore, improving light transmission by almost 40%.
This bump in performance now allows manufacturers to pack in up to 20 megapixels (so far) without compromising image quality not only in normal lighting conditions (day light, mid-day) but also in conditions where the light levels start to dwindle (sunset, or dimly lit rooms). So when you're out to buy a new point-and-shoot, it would be a better idea to invest in a camera with a backside illuminated sensor (denoted by BSI or BSI-CMOS).
Don't judge a camera or specially, a sensor by just the number of megapixels. The sensor type/ quality are much more important.
Watch out for more articles in the Photography 101 series.