View Vertex - Vertices
A Vertex (or Vertices if there are many) is a point that exists in 3D space within your scene. Vertices are typically used as corner points of polygons, and end or interior points of a line or curve segment. Typically, you do not see orphaned vertices in a scene, and if you do, its best to remove them with the Optimize tool. Some modeling tools will leave unassociated vertices behind, as is often the case when you delete polygon faces from a mesh.
In a sense, a vertex is the actual starting point or building block of any 3D mesh object, curve, and so on. The concept is intrinsic to any DCC application, as well as a foundation in geometry.
Vertices can be vexing things; double vertices (which coexist in the same space) are often responsible for odd shading occurences, both in the viewport and at render time. Unwelded vertices can dramatically impact a HyperNURBs mesh; if your results appear strange, start welding vertices and use the optimize tool while modeling.
Don’t confuse a vertex with a particle; they may be similar in appearance, but they are dramatically different “under the hood,” so to speak. And remember—weld and optimize.