The quality of connection is effected by multiple things, these include: You're internet provider, Ping to server, the server itself, and others in the server.
Now by what you described you have 3 bars, well the bars are never really detailed when determining ping connection. Typically once a players ping level gets close to 100 connection issues and lag starts to happen, anything higher then that and the situation gets worse. Though if it is not ping, then it is the game server themselves. If a server is not properly maintained in hardware and software it can cause problems that can make anyone lag. Basically you can be living right next door to the server with a direct line hooked up to it. But if any sort of problem happens to that server then you are going to get lag.
Another thing is other players. If they had bad ping then they can lag around in the game, of which you can see and be effected by it.
Also. One thing that many people do is confuse lag with FPS drops. Or Frame Rate drops. FPS drops are not effected by the server or enternet connection as a whole. But either a graphics card or processor that is having difficulty rendering/processing the game. This can make it appear as lag, but it is not.