Mesh / geometry
The raw shape of a 3D object: points joined into triangles. No color, no lighting, just form.
See it
What it is
A mesh is shape data and nothing else: a list of vertex positions plus an index list saying which triples of those vertices form triangles. Solid meshes get triangulated before the GPU rasterizes them, even a 'smooth' sphere (that ball is a few thousand triangles). Points and lines are separate primitives WebGL can draw too, but anything that reads as a surface is triangles by the time it reaches the screen. Vertices usually carry extra attributes along for the ride: normals for lighting, UVs for texture wrapping, sometimes vertex colors or bone weights.
You start caring about geometry when a model is heavy or looks wrong. Two levers: triangle count (the polygon budget, which drives both download size and framerate) and topology (whether the triangles are laid out in clean, even loops). Faceted low-poly can be a real style. Low-poly because someone decimated a scan badly is a bug you can read in the silhouette.
Gotcha: shape and appearance are separate things. A mesh with no material renders as nothing useful, and no material ever fixes a lumpy mesh. Also, vertex counts inflate for a reason: a vertex holds exactly one normal and one UV, so every hard edge and every texture seam splits the vertices along it. That is usually why the exporter reports far more vertices than your modeling app showed.
Ask AI for it
Model this object as clean quad-based geometry with even edge loops around curved areas, then triangulate on export. Stay under a 30k triangle budget, hold hard edges with supporting loops instead of relying on smoothing groups, and delete interior faces the camera will never see. Put the pivot at the base of the object, use real-world scale in meters, and export glTF/GLB with normals and a single non-overlapping UV set. No n-gons, no stray loose vertices.