This is a part of the fraction rite called the commingling. The priest quietly says the words “May this mingling of the Body and Blood of our Lord Jesus Christ bring eternal life to us who receive it.” It comes from an ancient sign of unity with the Pope. Many, many years ago the pope would share small piece of the body of Christ with other Catholic churches in the city of Rome. They would then commingle this in their chalices as a sign of unity with the Pope. While we don’t do this any more the symbolism is the same.
It’s also a symbol of the resurrection. Christ’s resurrected, yet broken body is reunited with his blood coursing once again through his body.