For those who care...
Pumps are one of the most popular styles of women's shoes, and they're also one of the most difficult to define. In their most basic form, pumps have closed backs, and low-cut fronts that hit closer to the toes than they do the top of the foot. A classic pump has a seamless vamp, and is without laces, buckles, straps or ties, but it's very common to see the classic pump silhouette enhanced by an ankle strap, t-strap, or mary jane strap. Pumps can have open toes, peep toes, pointy toes, round toes, almond toes or square toes, and they can have heels of any height.
Note that some of these may not quite qualify as "pumps", but going with a "heels" theme would open it up to sandals, loafers, platforms, etc. And we wouldn't want that, would we? No, sir.