Could have sworn that was it as well.. To be fair, the "The Game" section of the official ED website does say "Fight, trade, hunt your way across a giant galaxy of 100 billion star systems"...
This is because you could chose to define a star system in two ways I guess. As Cody pointed out above many stars have one or several companions. If you define the system as this
group of stars then the galaxy consists of approximately 100 Billion star systems.
If you however chose to define each
individual star as it's own system (since every star can potentially have their own planets orbiting) then the number would be approximately 400 Billion.
Doesn't really matter though since the human brain can't really comprehend these numbers anyway no matter which one you pick. There's simply put more stars out there than you could ever visit even if you played the game nonstop without food or sleep for the rest of your life.
In regards to the OPs question.
We live in a galaxy of the same size right now and we manage to meet up with each other just fine.

They are making it that big simply because they can and that happens to be the size of the Milky Way which this game takes place in.
Travel in ED is not done through warpgates but instead you have a hyperspace drive that has a certain range (couple of light years) based on what ship/engine you have installed that lets you jump to any star within the bubble. Trade, missions and a lot of other activities will also help drive people together. Another thing to keep in mind is that there is going to be a lot more NPC activity in ED compared to EVE which will help the universe feel alive even if there happens to be no real players around you in the particular area you are playing in.
As people already have pointed out. The DDF archive is a gold mine of information if anyone wants the specifics about this game.
http://forums.frontier.co.uk/forumdisplay.php?f=36
Reading about the background simulation might be a good starting point in regards to this.
Background Simulation