I sometimes see woodworkers talking about a zero-clearance insert for their table- or band-saws.
What is it? And why/when should I use one?
I can't think of a time when you wouldn't be better off using one. However, sometimes it's sort of a pain to make one for every blade, or in the case of a Dado set every blade combination... So it tends to not be used for non critical cuts sometimes. But again, I can't imagine it not helping for any cut.
A zero clearance insert is an insert which exactly matches the width of the blade. You can make one by slowly raising the blade through an un-cut insert.
The advantage is as aaron says, they prevent things from falling through the hole, and more importantly, they reduce chip-out by ensuring that the piece has support and thus chips won't tend to get pulled away from the board. It's not perfect though, so if you care, still put in your sacrificial piece. In general, the less open space you have under your piece, the more control you have over it when cutting.
You should always use an insert that leaves as little gap around the blade as possible.
Let me add a couple things:
They're typically made out of plywood or MDF to prevent wood movement.