Let me first introduce you to a couple of terms which will help you understand digital images better.
Pixels: Images are displayed in tiny blocks of color that together form an entire image. Such a ‘picture element’ is called a ‘pixel’. So, how we measure an image size in inches, say 5” x 4”, the computer measures it in pixels - 1024x738 pixels. To learn more about pixels, please click here.
Resolution: A measure of how tightly the pixels are packed together in an image, and is measured in dots (pixels) per inch or dpi. So a 1024x738 image can be of resolution 30 dpi, 300 dpi or even 3000 dpi. A 300 dpi image will have more pixels packed tightly together in the same inch of space than a 30 dpi image. So if we print the image at 30 dpi as well as 300 dpi, the lower resolution 30 dpi print having loosely packed pixels appears ‘boxy’ or ‘chunky’, whereas the higher resolution 300 dpi print having tightly packed pixels appears sharp and smooth. And no points for guessing that the size of the 300 dpi image, in megabytes (MB), is going to be far higher than the 30 dpi one. Click here for more on resolution.
The rule goes that for printing good quality images, the minimum resolution required is 300 dpi. Computer monitors are less fussy, and manage quite well with 72 dpi. You really can't make out the difference on-screen between a 300 dpi image and a 72 dpi one!
So, the take-home message is:
1. If you want to print the image, resize to a minimum of 300 dpi.
2. If you intend to share the image over the web, around 72 dpi should do.