Cove bits are the mirror image of roundovers, creating a concave profile. Useful and attractive in their own right for decorative edges on tables, they are often used in combination with other bits to create intricate moldings (nearly every molding I’ve seen incorporates at least one cove). Paired with a matching roundover, you can create rule joints for drop-leaf tables.
Like roundovers, cove bits are sized by their radius and are often sold in sets. As with most sets, you’ll likely find yourself not using the bits at each end of the size range; unless you regularly make a lot of molding or have other needs for concave routing, you’re probably better off getting multiples of the specific sizes you need. For creating coves on the edge of 3/4" stock, a 3/8" or 1/2" bit will prove the most useful.
Because they’re round (looking at a cove bit edge-on, it’s really a hemisphere mounted to the shank), there’s a lot of metal there, making for a heavy bit. Larger radius cove bits should always be used in a router table.