Its a reference standard for color. It lets designer pick a specific color and get predictable physical results in whatever their output medium is. A specific Pantone color has a set of metrics for displaying it electronically and a physical standard for what that color looks like as well. This allows ink manufacturers to define mixing formulas that produce a named Pantone color reliably.
Like if you wanted to print something with a specific green color consistently, you'd pick the Pantone based green in your design software. This allows the printer to either buy a specific ink which has been calibrated to produce that specific version of green which matches the Pantone standard. The ink manufacturers have done the R&D so that they know what specific ink blending is required to get that specific color of green, and it results in a recipe that printers can use so that they load up the press with that specific blend of ink.
Now that's spot color, it gets more complicated with process color (ie, dithering CYMK to produce a visual representation of the color spectrum for "full color" images). I think there's Pantone process colors, too, which help people maintain color consistency by using base color inks which produce consistent process color output, often with close matching of Pantone process colors and Pantone spot colors.
A lot of high end commercial printers can usually do press runs using more than 4 colors. Base CYMK for process color and then, if the job requires it, one or more spot colors for highly matched colors. Like if you were printing a promotional magazine for a sports team whose team colors were Purple and Gold. Chances are, the teams Purple and Gold are matched to Pantone spot colors. So the magazine would probably end up specifying the Pantone spot colors for solid color graphic elements that used those colors and then use Pantone process colors for the other full-color images. This gives you highly predictable, close tolerance versions of the team colors as well as color fidelity with process colors (photos, etc).
If you tear open a cereal box or look on the end flaps, you can often see the color targets they print. Usually you'll see CYMK and a couple of spot colors used.
Color printing is extremely complicated in the commercial world. It's not just a sort of general mix of CYMK like you'd get on a color printer or copier.