TMPCAR is a binary file which is generated during dynamic simulations and relaxation jobs using full wavefunction predication. It contains the ionic positions and wavefunction of the previous two steps. Those are needed for the extrapolation of the wavefunctions. It is possible to use the file TMPCAR for MD continuation jobs by setting the flag ISTART=3 on the file INCAR (see description of INCAR, section 6.14, 6.26).
Instead of the TMPCAR file VASP.4.X can also use internal scratch file. This is faster and more efficient but requires of course more memory (see section 6.26 for more details).