DEMs are files that contain either points (vector) or pixels (raster), with each point or pixel having an elevation value. They come in a variety of file formats, from .csv to .dem to .txt, and you can derive lots of other information - like contours or 3D surface models - from them.
There are a few terms that may be encountered that have subtle but key differences:
- DEMs: digital elevation models represent the land or "bare earth" (no trees, buildings, etc.)
- DSMs: digital surface models represent the reflective surface of the earth (bare earth plus trees, buildings)
- DTMs: digital terrain models are either synonymous with DEMs or comprised of a network of vector points instead of a continuous raster
- Further details here and here
This information is accurate for ArcMap Desktop 10.6, ArcGIS Pro 2.1.3, Global Mapper 18, and QGIS 3.2.1.