A term originating among expatriates living in Thailand, a visa run is a quick, one-day trip across the border of a neighboring country and returning. This is typically done on or the day before the expiration of one's visa. Exiting the hosting country and instantly returning "resets the clock" on a pre-determined visa length to allow the visitor to extend their stay in the hosting country. Some nations have different laws controlling one's ability to perform consecutive visa runs, such as shortening the length of the subsequent visa, or limiting how many times within a given number of months one can perform a visa run.
My 60-day Thailand tourist visa expires tomorrow, so I'm taking a visa run into Cambodia in order to stay another 60 days.
Stepping back then back again in a country over a short period of time (ie same day) - in order to reset/extend the period of days a non-resident can stay in a country.
Most foreign visitors to Thailand are granted a 30 day visa on arrival in Thailand. Staying longer requires a new visa, and the fastest & most economical means of getting it is a visa run: exit Thailand and return.