What does this indicator mean in the right bottom cornor of the official Bitcoin wallet?
That icon indicates the state of your connection with the rest of the Bitcoin network. "8 active connections" mean that you are connected to 8 other clients.

Since you got 3 of the 4 bars with 8 active connections, it is enough. As far as I remember, I always had 3 bars, so I guess it's the default setting. Probably, to get the last bar you will have to manually configure more nodes to connect with.

When you have 1 or 2 bars, there can possibly something wrong. Maybe your firewall blocks the port for Bitcoin (8333).