It's worth noting that bandwidth is only one aspect of a connection. It's important when data flows mostly in one direction at a time (e.g. when you download a file from a server), or when the data streams are independent of one another (e.g. during VoIP, your voice and the other person's can flow regardless of whether the other person is listening).
For applications where the next transmission from A to B depends on the last transmission from B to A (e.g. most games), the latency is more important. Even if your connection to Mars was 1 Tbps, you wouldn't be able to play a game with someone on it because light takes several minutes to make a round trip.