Mesh: A mesh is a 3D model made of many small flat faces, usually triangles, that together approximate the surface of a part, as used in STL, 3MF and OBJ files.
A mesh describes a shape the way a geodesic dome does: as a network of flat panels. Each triangle is defined by three points (vertices), and neighbouring triangles share edges. The finer the triangles, the closer the mesh follows a curved surface, and the larger the file.
Meshes are what 3D printers work from. A slicer cuts the mesh into layers, so the format suits additive manufacturing well. STL, 3MF and OBJ are all mesh formats.
Example: a cylinder 20 mm across, exported with 32 segments around its circumference, has flat facets about 2 mm wide. On a print with 0.1 mm layers those facets can show on the surface. Exporting with 128 segments makes them about 0.5 mm wide and much less visible, at four times the triangle count.
A mesh is an approximation, which is the main difference from a CAD solid in a STEP file. A STEP file knows a hole is exactly 10.00 mm; a mesh only knows where the triangles around it sit. That is why machining prefers STEP.
For a mesh to be printable and measurable, it must close up with no gaps, overlaps or flipped faces. That property is called a watertight mesh, and the stricter edge rule behind it is manifold. Read STL vs STEP vs 3MF for more.
Go deeper: STL vs STEP vs 3MF (and OBJ, DXF, IGES): which file to send for a quote