There are three "official" levels of twilight: Civil, Nautical and Astronomical.
CIVIL Twilight is considered the period during which it is still bright enough to go about your business as if it were still daylight (for example, the streetlights are still off, you do not need to turn your headlights on when driving). Most laws simply use a "30 minute" time period after sunset. I guess that this is the time period you should use in planning your party. Thirty minutes after sunset, some of your guests will find it a bit too dark, if you do not have lights on.
However, the real time changes with the seasons and with your location (specially your latitude). The scientific definition is that civil twilight ends when the Sun is 6 degrees below the theoretical horizon. At that point, the Sun is still lighting up the tropopause (the tropopause marks the limit of the troposphere, the layer of air closest to the ground, that contains all the usual clouds).
NAUTICAL twilight is (or was) the time when the sky became dark enough for some stars to be visible, while the horizon (at sea) was still visible. This allowed the navigator to measure the altitude of stars, using a sextant. The navigator needs to see the stars (it has to be dark enough) AND the horizon (it cannot be too dark). The scientific definition of the end of Nautical twilight is when the Sun gets to 12 degrees below the horizon.
ASTRONOMICAL twilight ends when the Sun reaches 18 degrees below the horizon. Until that time, the Sun still shines on the upper regions of the atmosphere (mesosphere, for example). We can't see it with our eyes, but astronomical cameras would still detect some diffuse light that would fog up astronomical pictures. Astronomers have to wait that long before they can take pictures of distant galaxies.