You might be surprised to hear that, until fairly recently, this was actually the 'correct' way to pronounce 'wh'. I had a reasonably formal British education and was taught by schoolmistresses who were born before the first world war. The teachers I grew up with made a distinction between 'witch' (pronounced with a 'w') and 'which' (pronounced with a breathy initial 'hw') and they taught us to do the same. Twentieth-century dictionaries also made this distinction clear. Who observes this distinction nowadays? Relatively few. It is a standard feature of Scottish accents, and of a few regional accents among older people in the US, I believe (thank you to Dan Smith for that information). There are also some RP speakers who still speak in this way.

It says they are using old-fashioned, careful, formal pronunciation. Fifty years ago in the United States it would have been a marker of "educated" speech. At one time, centuries ago, the "wh-" words were actually spelled with the h first, "hwen" instead of "when." I don't know why the order got reversed. The American Heritage dictionary lists both pronunciations: "wĕn," and "hwĕn," so the compilers believe both are still current. I will have to start listening carefully. Notice that it isn't necessarily an all-or-nothing thing; the "h" can be aspirated lightly.