DPI stands for dots per inch, it lets you know the resolution of the art file.
The higher the DPI the better quality your artwork will be.
But, that does not mean you can take a low resolution art file and then change the resolution to 300 DPI, it will still be a poor quality file.
The artwork has to be created at 300 DPI in the 1st place.
Great Quality Artwork would be between 200 DPI and 300 DPI
Medium quality artwork would be between 120 DPI and 200 DPI
Poor quality artwork would be below 120 DPI
In Photoshop you can see your DPI by selecting image size, and then looking at the Resolution field, make sure its set to Pixels/Inch and not Pixels/Cm.