A Canon 30D which has an 8.2 megapixels (MP from now on) sensor in it. I have had several people ask why I use something with only 8MP when their camera has XMP (X being between 7 & 10 usually). By the way 8.2MP would translate as 8.2 million pixels just to be sure we are on the same page.
The short answer with no technical jargon is because you are comparing apples to oranges and the sensor in a point and shoot is not comparable to the sensor in an SLR.
The semi technical answer has more to do with the size of the sensors and the electrical issues that stuffing all those pixels onto a sensor cause than anything else. Take a look at the image showing a comparison of the most common sizes of image sensors in digital cameras. There is a good bit of difference between the full frame and APS-C sensors (most common in digital SLR cameras) and a large amount between APS-C and a typical point and shoot. There are some other sizes but there is not a lot of difference in them if we don’t include medium format and larger which we aren’t, so for the sake of simplicity I left them off the chart.
So as you can see putting 8.2 million pixel sites into a tiny sensor means that the pixel sites must be smaller and closer together. Smaller pixel sites means less light can make it through the opening to the pixel sensor and the lens needs to be able to resolve enough information to have usable detail in those tiny areas. You also start having problems such as the random movement of the electrons that make up the materials in the pixel site. See when a material is above absolute zero (-273 centigrade) the electrons move randomly, with such a tiny bit of light hitting the pixel site the movement of the electrons can become an issue. The next issue is that the tiny pixel sites do not collect much light so the amount of signal they receive is very small. To help compensate for the small signal the pixel site are given more electric charge so they are more sensitive. The higher electrical charge causes more heat buildup and that means more noise in the final image.
As an example the two images below are cropped pieces of the overall image shown at 100% image size so you can see the detail of the image better. Both pictures were taken at ISO 400 in aperture priority mode set to f5.6. The one on the left is the full image the middle is from my 30D and the one on the right is from my Wife’s Canon PowerShot A710IS (7.1MP) the red rectangle shows the cropped area.