The set of partial differential equations governing fluid flows and heat transfers are not amenable to analytical solutions, except for very simple cases. Therefore, in general, in order to analyze fluid flows, flow domains are split into smaller portions (made up of geometric primitives like hexahedra and tatrahedra in 3D, and quadrilaterals and triangles in 2D) and linearized governing equations are solved inside each of these portions of the domain. Care is taken to ensure continuity of solution across the common interfaces between two portions, so that the linearized solutions inside various portions can be out together to give the fluid flow in the entire domain. Each of the portions of the domain are known as elements, and the collection of all elements is known as mesh or grid. The origin of the term mesh (or grid) goes back to early days of CFD when most analyses were 2D in nature. For 2D analyses, a somain split into elements resembles a mesh, hence the name.
Mesh generation is the field of CFD which deals with creation of meshes from given domain definitions. There are various classifications of meshes, and mesh generation can be a very complex process in itself. Meshes can be classified based on on or more the following criteria (maybe even more):
i) Dimension (2D or 3D) ii) Connectivity (structured or unstructured) iii) Element types (tetrahedral, hexahedral or hybrid) iv) Inter element connectivity (conformal or non-conformal)