To snigger is to laugh quietly and badly. Three parts to it. It is small and half-hidden — through the nose, behind a hand, a shaking of the shoulders rather than a real ha-ha. It is unkind — someone has made a mistake, or fallen over, or said a word that sounds rude, and you are enjoying it at their expense. And it is often at the wrong moment: in class, in a meeting, at a funeral, exactly where laughing is not allowed, which is part of why it has to stay quiet. Schoolchildren snigger. Grown-ups sniggering sounds childish, and that is usually the writer's point. It works as a verb (they sniggered) and as a noun (a snigger went round the room), and often comes with at: they sniggered at his accent. One important practical note: snigger is the British spelling; American writers use snicker, which is the same word said a different way. In the United States, snigger is now avoided in speech and print because it sounds close to a racial slur, so if you are writing for an American reader, choose snicker. In Britain the word is ordinary and carries no such shadow.