Mesh analysis (or the mesh current method) is a circuit analysis method for planar circuits; planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other. A more general technique, called loop analysis (with the corresponding network variables called loop currents) can be applied to any circuit, planar or not.
Mesh analysis and loop analysis both make systematic use of Kirchhoff’s voltage law (KVL) to arrive at a set of equations guaranteed to be solvable if the circuit has a solution. Similarly, nodal analysis is a systematic application of Kirchhoff's current law (KCL). Mesh analysis is usually easier to use when the circuit is planar, compared to loop analysis.