Remember way back when when we explained how CMYK color worked? Didn't think so.
Well, when you're printing in color, chances are you're doing so by using 4-color process printing (C: Cyan, M: Magenta, Y: Yellow, K: Black). 4 plates are created (one for each color) with a very precise halftone pattern. Then, when the colors are overlayed, it creates the illusion of full-color.
But what if your job calls for only 1 or 2 colors? Or what if your project needs to use a very specific color? Then turn to spot colors!

Let's say you're printing letterhead and your company's logo consists of black and purple. You could use process printing, but then you'd have to create at least 4 plates to approximate those colors, which would bump up the cost of printing. Instead, you can specify those two colors using a Color Management System (Pantone is the industry standard, but there's also Focoltone, Toyo Ink, and TruMatch. It's a preference thing.) or by working with your printer to produce an ink color that matches what you're looking for.
Spot colors are standalone ink colors. Instead of combining 4 colors to get purple (C: 75%, M: 100%, Y: 3%, K: 2%), you designate a particular ink (Purple = Pantone DS 168-1 C). This is also beneficial because it allows for greater color consistency.
If you love a particular orange, find the appropriate standard spot color (Pantone DS 67-1 C) and make sure that you use only that orange whenever you print your marketing pieces. Because of the standardized Pantone color system, most printers will be able to approximate that color and your marketing materials will always look consistent.