This is someone who might buy whatever it is you are selling. Apparently this usage of the word came into vogue at some point after 1913. Prospects come with various degrees of thermal energy, but the warm ones are the best.
For instance, if you're in outside sales, you know that you are constantly bombarded with outfits trying to sell you lead lists. These are lists of names and phone numbers (at least) of folks in your area who fit a certain profile. The more you pay for these lists, the more information they are supposed to contain. You can buy a list of females in a certain zip code who are between the ages of 40-50 and who have a net worth of over $100,000. Did you know that? That was just an example. You can tailor the request for information any way you like. I could request a list of angst-ridden geeks with no lives between the ages of 14 and 22 and I'm sure I'd get some of your names. But what good would that do me? You're not going to buy anything from me. And, sadly, neither are any of these other folks on these lists, no matter how appealing the demographic might appear. The reason has to do with thermal energy: These are just cold leads, not hot prospects. I'd have to call a hundred of them to get one of them to talk to me. That would not be productive use of my time. (Quit laughing. I'm really not on this site as much as you think. . . OK. Maybe I am. Shut up.)
The hot prospects come from personal interaction of some sort. The most often used method of obtaining hot prospects comes from referred leads. It is incumbent upon a good salesperson to always ask for referred leads after making a sale. It's a hard thing to do, because the inclination is to not say anything that might screw up the deal you just closed. What a good salesperson has to remember is this: You have the check in your hand, don't you? You have the signed paperwork, don't you? So this prospect is now dead. You've turned this one into a sale. What are you going to do tomorrow? If you don't replace this one with a live one, you're out of business. So get with the program here: Tell yourself that you did a good job and you helped these folks. And then ask them for a list of people they know who might be in need of your services. Until a salesperson gets in the habit of doing this every time, it's good to have a pattern of behavior that he uses every time. Here's a good one:
Take out a sheet of paper. While you are telling the new clients how much you appreciate their business, start writing on the sheet. While you're writing, tell them that they know folks whom you do not know who might be in need of your services. They won't be able to see what you're writing, but just draw some lines and number each line. How many? Depends on how secure you feel. But at least 3. Never any less than 3. Then hand them the sheet and ask them to write down the folks who came to mind when you said this. You might not get any. You might get very surprised and have the new client hand you their address book and say, "Hell, here's everyone I know. Call 'em if you like." I've had that happen. Either way, this is the only way to get some new hot prospects.
How will it turn out with these new prospects when you call them? Every sales field has its own set of "magic numbers." In mine, it's 10 - 4 - 1. You call ten of them, four will actually talk to you, and one will buy something. But when that one buys, remember that you're out of business until you replace him or her with another hot prospect.
I suspect that this use of the term comes from "prospective buyer" as opposed to prospecting for gold, although it's easy to see how some could make that mistake.