A DEM is a raster dataset that represents elevations over a defined extent. Raster data is made up of a series of equal-sized cells, with each cell containing a numeric value. What the value represents will depend on the purpose of the raster.
In the case of a DEM, the raster cell values represent the average elevation for the area covered by the cell. The following screenshot is an example of a DEM:
As you can see in the previous screenshot, if you were to zoom in on this DEM at some point, you would start to see individual squares that are the cells making up the raster data. The squares you see are now commonly referred to as a pixel, even though that is not correct. Each cell is assigned the value of the averaged elevation it covers. The cell might be 1 foot x 1 foot, or 2 meters x 2 meters. It is the size of the cells that determines the resolution and plays a part in its accuracy.