Praise be to Allah.
Burping refers to when air comes out from the stomach, making a sound, through the mouth when one is full.
Simply burping does not break the fast, but if some food comes out with it, then it must be spat out. If it is swallowed deliberately, then this breaks the fast, but if it is swallowed involuntarily, without meaning to, or if one cannot spit it out, then the fast is still valid.
Al-Ramli said in Nihaayat al-Muhtaaj, 1/171:
He ate and drank a lot at night and he knows from experience that when morning came he would burp and something would come out of his stomach as a result. Should he be told not to eat and drink so much, and if he goes against that and something comes out, does that break his fast or not?
This is subject to further discussion. The answer is that he should be told not to eat too much at night and when morning comes, if he burps and something comes out, but he spits it out and washes his mouth, that does not break his fast, even if that happens many times.
See also question no. 12659
And Allaah knows best.