Most pictures on a screen are made up from small dots of colour. Each picture is made up by a certain number of dots or pixels. Quite simply the higher the number of pixels the higher quality the picture and the larger it can be displayed or printed without distorting. If a picture is enlarged beyond a certain point it will begin to distort and appear blurry.
A screen displays at 72dpi (dots per inch) where commercial presses print at 300dpi. You will need to start your artwork at 300dpi in order for it to print cleanly without blur. If you do your artwork at 72dpi and change it later to 300dpi it won’t fix the problem.