Press that to bring up your list of 12 friends (represented by kaleidoscopic multi-coloured circles) for quick message or call access. Twiddle the Digital Crown to get around your circle of trust, and tap to select the special one.
A long press of this very specific button also turns your Watch off.
You don’t have to keep putting down and lifting your arm to get the screen to blink to life. You can just tap on the screen to wake your Watch. Tap works the same way as it does on your iPhone, so if you want to select something, just tap it.