What Does 'Border Bounce' Mean in Thailand?

Your definition is almost close. A border bounce is when a person leaves Thailand, by land, crosses over to another country, enters that country legally, and then crosses back into Thailand.

Generally the only time you would border bounce is:

a. To activate another 60 (or 90) day entry on a multiple entry visa (depending on the type of visa)

b. To get a 30 day visa exempt stamp.

This requires getting the legal right to enter the other country; generally through a visa on arrival (Cambodia or Laos), or a day pass (Myanmar). I'm not familiar with Malaysia's system.

For the Thai side, it is not required to stay the night out of the country. I know some parts of Malaysia and Cambodia require a person to stay inside the country overnight before returning.