An ansatz is a tool used in trying to locate solutions of a given form. One writes the solution in terms of other unknown functions in a manner specifically designed to emulate the desired form, and then rewrites the equation in terms of these unknown functions. This can be particularly effective when one or more of the unknown functions are believed to be small or otherwise negligible, as one can then hope to treat their influence using perturbation theory.
If the ansatz has more degrees of freedom than the original fields, then one gains the ability (at least in principle) to insist upon a number of additional constraint equations to make up the difference. Typically, one exploits this ability to improve the structure of the equations as much as possible.