It can take on hundreds of forms including altering the tones, hue or saturation of all or parts of an image, removing unwanted detail and flaws, increasing detail in areas where that's desired, and combining several photos to create a final image that appears to be a conventional photo.
Before computers, this work used to be done at a less sophisticated level by photographers in the darkroom or by retouching.
These sort of things have been done for hundreds of years by artists.
Study the paintings of the grand masters. They were hired by the rich and powerful to paint their portraits and often their possessions. They painted to please their employers. Their skin and hair appears flawless. All at a time when people bathed infrequently and lacked skin and hair care products. Do you really believe they looked that good? Never a zit. Every hair in place.
Cameras don't capture an image the same way we see and especially the way we remember. They can't record detail in shadows and bright areas that we see easily, but they do capture every pore on a face, every piece of dust or tiny scratch on a product and every tiny piece of dirt or trash in a scene. The trouble is, this isn't what we notice or remember. These flaws weaken communication by being distractions.
That's why the best photos are almost always digitally enhanced. By eliminating flaws and unwanted detail and enhancing detail where desired, it's possible to create compelling images that actually appear more realistic than those that aren't enhanced. When done properly, it's all invisible.
See some before and after samples of digitally enhanced photos by Photoshop expert Richard Quindry.
Learn more about how digitally enhanced photos are made: Photoshop Expert Techniques