Like it says on the box! I have several wordpress installs on my local dev machine. For most of them, JETPACK_DEV_DEBUG works fine. For one of them, it does not work, and the site shows the wordpress.com connection and stats and all that. Jetpack 2.2.5.
Also, my hostname for all of these installs is 'localhost', which I understand is supposed to trigger JETPACK_DEV_DEBUG automatically? It does not do that for any of them.