Pseudo time-stepping, probably better known as pseudo-transient continuation, is the technique of solving for the steady-state solution of time-evolving partial differential equations by setting an initial guess and using a time-stepper to evolve the solution forward. It tends to succeed where standard globalization strategies fail by taking advantage of the natural structure of the problem.
My advisor, David E. Keyes, coauthored a few papers discussing pseudo-transient continuation. I don't think any of them are purely introductory, but his writing style is very clear. You might try: Convergence Analysis of Pseudo-Transient Continuation for a more comprehensive description and discussion.