Literal translation
to laugh until one's navel bursts
Meaning
to laugh long and loud
Explanation
Laughing a lot and very hard, literally laughing until the navel bursts. Laughter shakes the body, hence several expressions imagining exaggerated physical consequences. The word embouligue, navel, long common because it names something familiar and intimate, is now dated but survives well in this expression, felt to be a funny word. On the same pattern exist rire à se péter le bédélet, the belly, or rire à se faire péter la sous-ventrière, the girdle.