Broccolini, also called baby broccoli, is a naturally-occurring cross between broccoli and gai lan (Chinese kale). Broccolini is a trademark of the Mann Packing Co. and is described by their site as "Sweet Baby Broccoli".
Broccolini has long, thin stems with loose florets of green buds similar to those of broccoli. It also includes a few leaves, although fewer than the Chinese kale it's derived from. It has crunchy stems and a mild flavor.
Broccolini can be eaten raw, but it is most commonly cooked. It can be roasted, sautéed, steamed, grilled, or blanched. The tougher ends of the stalk should be removed before cooking.