A high-resolution image is often used for print products like flyers, brochures, and business cards, as well as for digital assets like websites. It is usually around 300 DPI (dots per inch). A high-resolution image is determined by its number of pixels. More pixels means sharper images and therefore, higher resolution.
For websites, when one mentions high resolution they mean at least 1000px on the shortest side so the image is clean and crisp.
Monitor screens with retina displays has four times more pixels than standard screens. For example, a 400px x 300px image (120,000 pixels) should have an 800px x 600px alternative (480,000 pixels) to render it well on a high-resolution retina display.