Almost everyone's answer here is correct, but none of them have actually answered YOUR question: "Nutritionists tell us we should eat more "green leafy" vegetables. Does this mean only the various lettuce types, spinach, and silverbeet?" So here goes: Green leafy vegetables include: Kale, lacinato, collard greens, all types of cabbage, Brussels' sprouts, bok choy and all Chinese greens related to bok choy, dandelion, mustard greens, turnip greens, watercress, spinach, beet greens, Swiss chard of any color or type, all lettuces, all microgreens including rare ones like mizuna, frisee, mache (Lambs' lettuce), rapini, arugula or roquet, escarole, chicory of any kind including endive and radicchio (which is actually red, not green...), any type of cress, cowslips and any other wild-crafted green you might come across such as plantain, fiddleheads, clovers, dock, etc. etc., etc. Truly, the term "green leafy vegetable" really speaks for itself and is VERY clear.
Broccoli is actually the flower head of the broccoli plant, but because it is green, has leaves attached (which you can eat) and has a nutritional profile much like the other leafy green I've mentioned above, especially those in the Brachonid/Cruciferae family, I think you're okay to call broccoli a "green leafy". You could perhaps push that to include cauliflowers of all colors, too.