This is an old tradition and I read different stories about where it comes from. Basically older Russians believed that spirits (read about "Domovoi" in Wiki) inhabited their houses and those spirits didn't want people to leave their houses and leave the spirits alone. So the tradition was to have a seat before a trip, so that the spirits thought everything was just as usual, got busy with their spirit-home-stuff and didn't notice that the people were gone.
Today I guess the reason for the tradition is as follows: before a trip you are usually in a hurry, trying to prepare everything and get everything done, so many things to do. So this have-a-sit is the last chance to sit quietly, calm down, think again if everything is ready, so that one could start the way light-hearted. Well, also light-hearted because the home-spirits are distracted with doing their things.