Image resolution (dots per inch or just dpi) is an indication of the quality of an image. It is less important for screen images but more so for printing. Common image resolutions include 72, 120, 300 and 600 dpi (dots per inch). When producing graphics for web pages or for viewing on the screen then 72dpi is generally the more popular resolution (and keep the images to less than about 30K). For scanning and printing, 400dpi is a good quality resolution.
For printing 100dpi is generally exactly 100 dots per inch. On screen however this is not always so, as it depends on the resolution of the monitor (so a 72 pixel wide image on a 17" monitor at 640x480 might come out at about an inch but at 1280x1024 it will be half the size, and so about 144dpi).
When scanning or printing dpi is something that becomes important.
For images meant for display on a screen, as in web design it is the pixel dimension that is more important. Consider two images that are both 100x100 pixels, but one is say 100dpi and the another is 300dpi. They will be exactly the same size on your monitor but when printed the first image will be 3 times larger then the second.
The GIF format doesn't store any dpi information--only the pixel dimensions so when the GIMP saves to GIF you ``lose'' your printer settings! When opening a GIF the resolution will be set to 72dpi.
When designing for screen display of images consider what monitor size will you want to design for (640x480, 800x600, 1024x768, etc). Then ensure your final image is not any larger then your screen. You will also need to take into account that the actual area of your browser is smaller then the screen and so you should keep images as small as possible.