Pixels are tiny light sensitive panels that form your sensor. The "… millions pixels" that your camera has is based on the total number of pixels that the sensor is made up of.For example a 12MP camera will have a sensor with the rough dimensions of 4288 pixels on the long edge and 2824 pixels on the short edge, multiplying thses dimensions together will give the total number of pixels.

Does the number of pixels matter?
On the whole, no. I you are wanting to blow images up supersize, then perhaps. A better question would be "does the size of the pixels matter?" to which the answer would most definitely be yes!

So, why does pixel size matter?
Each pixel has one role; to capture as much light as possible. The bigger the pixel, the more light and qualitative light it can capture. This is why a DSLR will always produce a better exposed, balanced image than a compact even if both cameras have the same number of total pixels. The sensor on a DSLR is considerably larger than on a compact, thus if both have the same number of pixels, those on the DSLR will be bigger.
For a much more in-depth narration on pixels and why they do or don't matter, take a look here at Ken Rockwell's "The Megapixel Myth" it's quite enlightening!

Which DSLR should I buy?
Choices choices! We shoot on Nikon, but in terms of quality there's really nothing much separating the two main brands higher up the end; Nikon and Canon. I must also mention; Sony, Olympus, Pentax….. but I've not had any practical experiences with these brands.

However, as a starter, Nikon for me has the best camera, the great D5000 - which superceded the D40 and then the D60 models. The D5000 is an excellent camera and can offer image quality similar to that of the more expensive prosumer models the D90 and D300 as I believe they use the same sensor. It's a fast and quiet camera with the excellent Nikon menu system (which for a newbie, I'd say was easier to navigate than Canon's and hence the recommendation).

The ADR (automatic dynamic range) is the same as on the D() models upwards and works a treat. It basically manages contrasts in colour and light so much better and really brings out striking images. Nikons are much better in producing balanced, rich, JPEG images than Canon as a rule.
The D5000, also comes with video (although it's not great and you can't manual focus while in record mode) and live view - the same as using a compact - and the rear LCD also flips and swivels. 

The last important note; go an pick one up! You really won't know what will suit you until you try it. If you want some comparison then take a look at the Canon 1000D or the 450D which are around the same price bracket and both are excellent cameras.

Prices from Warehouse Express;
D5000 Kit   £509
EOS 1000D £364
EOS 450D   £531 (Amazon)

This is not meant as a thorough complete guide nor is it particularly endorsing one brand over another but purely based on my own current experiences with each.

Gareth