In design (and any other digital displays), resolution has to do with the number of pixels in an image. The higher number of pixels in your image the higher the quality.
Let’s say you have an image that’s 200 x 300, this means the image is only 200 pixels across your screen and 300 pixels deep. That’s why, when you resize any image larger than it’s original file size (maybe 200 x 300 to 400 x 600), the image gets pixelated. The image was forced to ‘make up’ filler pixels, causing an ugly, grainy image.
An image can also have a measurement of PPI / pixels per inch (pixels for web) and DPI / dots per inch (dots for printing ink), again, the higher the number of PPI/DPI the higher quality the image. Typically, 300 dpi is best for printing and 72 ppi is best for web.