Those two numbers denote how many pixels, or individual dots, make up the image on your screen. The first number signifying the number of horizontal pixels, the second signifying the number of vertical pixels.
It goes without saying, the more pixels to keep updated, the more computing power needed, but you only ever see the effect of hardware strain in games. The reason why everything gets smaller in Windows when you increase the resolution, is that with more dots on the screen, you're moving all the dots slightly closer together.
In games, the higher the resolution the better, but you may find the frame rate suffers if your hardware can't cope. Framerate being the number of still images per second that are put together to make motion in games. Logically, if more pixels are in each picture, the longer time it takes to draw it, so when you add them all together, the computer can't draw as many frames per second as with a lower resolution. There are plenty of other things that affect framerate, but resolution is one of them.
