I've seen the term "burp" used, for example, in a description of the Saturn V F-1 engine start sequence (or what is perhaps the source document - see pdf p 62, source page 4-9). What does it mean? What causes it to happen?
"Burping" usually refers to a start-up failure mode in which the combustion chamber pressure rises too quickly relative to the pressure of the inflowing propellants (as the pumps spin up, for example). This can cause the feed system to backflow with undesirable effects upstream. Page 77 of this document contains an example of someone using the term in that fashion.
That said, it's not clear to me how ignition of the gas generator exhaust in the engine bell of the F1, as quoted in your link, would help to prevent that. The link seems to have quoted from and slightly changed an Apollo-era diagram found in Stages to Saturn, page 111. In the original it reads
Fuel-rich turbine combustion gas is ignited by flame from igniters.
a) Ignition of this gas prevents backfiring and burping
In this case I believe the writer is referring to the combustion chamber of the gas generator (which could, of course, be affected by "burping").