To sidle is to walk, but in a way that's casual, quiet, and a little sneaky. If you want to surprise someone, sidle up to them and say, "Boo!"
There’s a TV show where a character’s coworker has a habit of walking so softly that he constantly startles her — she never notices him coming. So of course she buys wrestling shoes and tries to sidle back! Sidling is a type of walking that is super quiet. If you want to leave a party without people noticing, sidle out the door. Sidling is a good way to slip away.