The short version: you leave Vietnam by land and come straight back with a fresh visa stamp.
You are in Vietnam on a tourist visa. It is about to run out. Instead of flying home, you take a van or car to a land border crossing, walk into Laos or Cambodia, and then walk back into Vietnam with a new entry stamp. That stamp gives you another 30 or 90 days, depending on the visa you arrange.
The whole trip takes one day. You leave early in the morning and you are back in your city by evening.
There are two main land crossings for visa runs:
You pay for transport and the new visa. Transport runs between 1.5 and 7 million VND depending on shared van vs private car and your city. The Cambodia visa fee is around 1.1 million VND at the border. A 90 day Vietnam e-visa is roughly 2.4 million VND if you want to apply for one during the run.
This is why most people do a visa run. While you are at the border, your driver or fixer can file a 90 day Vietnam e-visa application online. It gets submitted the moment your passport is stamped out of Vietnam. The e-visa comes back by email a few days later, giving you 90 days instead of the standard 30.