What does this indicator mean in the right bottom cornor of the official Bitcoin wallet? Circled in red:


When I hover over it I get the message "8 active connections to the Bitcoin network". Should Is this number too low and how do I change it?
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).