What does %~dp0 mean, and how does it work?

I find %~dp0 very useful, and I use it a lot to make my batch files more portable.

But the label itself seems very cryptic to me... What is the ~ doing? Does dp mean drive and path? Does the 0 refer to %0, the path to the batch file that includes the file name?

Or it is just a weird label?

I'd also like to know if it is a documented feature, or something prone to be deprecated.