You need a connection so that Market data, transactions, Matchmaking (I know... It's odd. I'll get to that), discovery data, etc. can be used. When you log in to play, your account goes to Authentication and you are moved into a game server, Selecting ANY option (Open, Private, or Solo) other than the training missions will place you in matchmaking so the game knows where you are. When you make a purchase, your transaction pings the Transaction server and the item is purchased and your credits are deducted from your account (we all have a Bank of Zaonce account. Deal. Wasn't my first choice but I had to get a Sidewinder somehow and theft is often frowned upon.). As you enter a system, your game downloads market data for the Commodity Market, Missions are downloaded, and NPCs are spawned depending on the system's population and economic state.
Edit: Also the data needed is incredibly low. I was seeing less than a kilobyte (bits really. less than a Byte.) while I was out in the black but I haven't check the connection since. Still really low though so don't worry.