Red light means you're not connected to broadband. If the broadband light is red you've failed to login to. The lights on the BT Hub tell you what's going on with different functions and whether there are any problems. When it's green and steady, everything is fine. However, when it blinks red or stays solid red, it signifies a Loss of Signal, a problem preventing your router from communicating. I've been without full fibre since yesterday (which stopped suddenly) which I require for work. An open reach engineer is scheduled for Tuesday (4 days). Green and blue are generally regarded as good colors, whilst red, orange, and purple aren't. In my case, in the outside grey box, the splice between the internal and external fibre optic cables had separated and hence the problem. There's a power light which might be green or flashing green (booting up), red (offline), orange (identifying a problem) or blue (working normally).
[PDF Version]