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In blender a Mesh can be a four sided plane a six sided cube or look like any object you see in real life. Its basically a 3D object whereas a light or camera is not a mesh.
Render / Rendering
Rendering is to output the 3D scene as an image or movie file.
Texture Map / Texture mapping
A 2D image or Photo used to cover a 3D object
In blender Vertices can be seen when you have selected an object and then choose edit mode, they appear as little dots in all corners of a cube for example. A cube has 8 Vertices and more complex meshes can contain many thousands.