It is very unpleasant. "Holiday tummy" is another name for "traveler's diarrhea". When people go on holiday they sometimes get sick because of the change in their regular food and diet. They get nauseous, have stomach aches, and sometimes get a real bad case of diarrhea. So when you get sick like this, you probably have "a bout of holiday tummy".

It also means that the speaker is a speaker of British English. Americans might say "Montezuma's Revenge", in reference to the last Aztec ruler who ruled Mexico before the Spanish conquered it.