dpi - how do they affect an image?

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I don't know how dpi (dots per inch) affects an image.
When you start a new file in Photoshop you can set the dpi to your liking.

for example you have a square canvas of 1,000px (width and length) setting the dpi to 100 or 300 doesn't show any changes. Does this have an effect on printing somehow?
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Hmm ... DPI helps to smoothen pictures .... the higher the DPI the better the result .... normally 300 dpi is good
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Tegumi "im always cute"
http://en.wikipedia.org/wiki/Dots_per_inch#DPI_or_PPI_in_digital_image_files