A sabiki rig, sometimes called a piscatore rig, is a set of small lures typically used to catch fish that eat small prey.
A sabiki is typically fished off boats, piers, jetties, or any structure over the water. Sabikis consist of any number (usually between 6 and 10) of small hooks, each one on an individual dropper line which are a few inches long. The individual dropper lines are then tied to a longer leader in series, about 6 inches apart; a weight is tied to the end of the leader. The individual hooks are decorated as lures or tied like flies similar to those used in fly fishing. Often they have a simple piece of metallic or iridescent film attached to them. On any individual rig all of the lures will be identical. The type or size sabiki used depends on water conditions, species of fish sought or simply the angler's preference.
You can also attach a bait cage and bobber to the rig and catch fish like large flathead mullet or Short mackerel. In Japan, they are used to catch sardines and mackerel off of large piers. If you have a bait cage on the rig you should give a large jerk (as if you were setting the hook) to release the bait. 
Sabiki rigs with their many small, sharp hooks are easily tangled and can be a nuisance to the angler. If they are not handled carefully the angler can be hooked. This can be avoided by using a sabiki rod. A sabiki rod is a hollow fishing rod with a funnel shaped tip. The line is fed from the reel through the hollow body of the rod and out of the funnel shaped tip. When the sabiki rig is reeled in the hooks and leaders are drawn directly into the rod where they will not tangle or injure the angler.