When you cast a lure with a teaser in front of it, you are using a large lure and a smaller one at the same time. The teaser fished in front of the larger lure looks like a small baitfish being chased by a larger one. Sometimes you can catch a double header.
The teaser shown on the bottom is a Red Gill, and is considered a good sand eel imitation.
If you are going to be throwing lures, you can add a teaser and be throwing two lures at once. Maybe you will catch a double header.
You may not be sure if the stripers are feeding on large baitfish, or small ones. When you use a teaser, you are using two different size lures at the same time, which is a distinct advantage. Also, when retrieved from a stripers viewpoint, it may appear that the lure (the larger baitfish), is chasing the teaser (the smaller baitfish). Now the striper has two choices, but you don't. You will catch the striper regardless of which the fish chooses.
Teasers add a little drag, so if the teaser is going to keep you from reaching the fish with the cast, then omit it. Also, bluefish can bite off the teaser, so you may not choose to use them when bluefish are around.
AVA 17 and Teaser
A really good time to use teasers is when sand eels are around. Use a narrow metal lure like an AVA 17 with a teaser ahead of it. The AVA 17 provides a casting weight while also looking like a sand eel. So you are fishing with two sand eel imitations at the same time; the AVA and the teaser. When you retrieve this combination, the AVA stirs up the bottom similar to a sand eel digging into the sand.
Although streamer type flies are normally used for teasers, many small narrow soft plastic lures make good teasers.
I usually mount my teasers on a dropper loop located about 20 inches ahead of the main lure. The lure then serves as a casting weight for the teaser.