PERT was developed in the late 50s by Booz Allen Hamilton to manage the Polaris Missle Project which was considered very ambitious for its time. This is what the PM history texts credit and I'm sure it evolved over time since its very logical. I adopted PERT-like estimating techniques long before I knew about the existence of PERT.

The main strength of PERT is that it uses a multiple estimate approach that allows one to compute a level of confidence that the estimate will be met. You can apply it to both cost and budget estimates.

PERT is still relevant today and often used informally by project managers not knowing the details. These project managers ask estimating questions like "what's the worst case?" or "if everything goes well, will your estimate improve?". They put together estimate ranges when planning the budget and timeline to let the project sponsor know there will be some variability in any big project.