What do ringing the bells denote at communion in the catholic church?

They are an audible alarm meant to draw your focus as to what is going on up on the Altar. They are sounded at the moment of transubstantiation when the bread becomes the Body of Christ and then later when the wine becomes the Blood of Christ. It is a serious (mortal) sin to deliberately be paying attention to something else when this is happening if you are in the Church. It is a lesser (venial) sin if you did so accidentally. Thus, the bells are a sort of a service for you to help you not sin.