It is all about the number of pixels in your image. Think of a pixel as a tiny square of color. If you want to print a 8" x 10", you need a lot of pixels; if you want to print a 4" x 6", you need fewer pixels. Look at the file's properties to see the pixel dimensions. Most photo-editing programs let you see the image attributes in pixels, inches or centimetres.
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Since the human eye cannot detect individual squares of color if there are 300 or more in an inch, it makes sense to have 300 ppi (pixels per inch*) for images at their final printed size.
So then, for a 8" x 10", your image requires at least 2400 x 3000 pixels. This will give you a high quality print.
Let's say your image is only 800 x 1000 pixels. No one can stop you from printing it at 8" x 10" size, but now you will see a noticeable drop in quality - "pixelation" - you can detect individual squares of color.
Dividing the pixel width and height by 300 determines the maximum size you can print your image at high quality.
This is why web images don't make good prints. There are not enough pixels. A digital camera, set at VGA resolution (640 x 480 pixels) takes perfect size images for the web.

Dividing by 300 ppi, you get 2.1" x 1.6". This means that this web image would print clear and crisp at a size of 2.1" x 1.6". That's quite small. If you try to print it at 6.4" x 4.8", it will be pixelated.
Keep in mind that when you crop a photo, you are discarding pixels. Check the new pixel dimensions to verify that you still have enough pixels to print it at the desired size.
* Although many people use ppi and dpi (dots per inch) interchangeably, dpi takes on a different meaning when used to describe printer quality settings. For example, you can set your inkjet printer to print at 1200 dpi. However, 1200 dpi is not the image file's resolution.