We are really into Communion symbolism now. Just after sharing the sign of peace with one another, the priest breaks the host and drops a piece into the chalice. What is going on here?

This is yet another expression of communion. First, the actual breaking of the bread, which is called the Fractio, was really just a very practical action of dividing up the consecrated bread for the purpose of distribution to those attending the Mass. It wasn’t until about the 900s that small individual hosts were produced that made the big ceremony of breaking the bread unnecessary.  So, now this action became more symbolic, rather than practical.

Just as Jesus broke the bread and gave it to his disciples, so the priest continued this practice in a symbolic way (Mk 14:22). The Didache (9:4) has this beautiful line about the origins of the bread we use at Mass: “Even as this broken bread was scattered over the hills, and was gathered together and became one, so let your Church be gathered together from the ends of the earth into your kingdom.” That bread, which was once many grains, has become one body. As St. Paul tells us (I Cor 10:17), “Because the loaf of bread is one, we, though many, are one body, for we all partake of the one loaf.”

This one loaf is broken for us and is a symbol of our union with one another, both in its origins and in its distribution. That Eucharist came from us and now comes back to us to create and nourish our unity as Communion.

But why the small piece into the chalice?  Apparently, in the early Church the bishop would send a piece of his Communion to his local priests to represent their unity as the local Church. The priests would then place that piece into their own chalices. 

It seems that around the year 190 AD, St. Irenaeus was urging various parties disputing the date of Easter to get along. He recalled a time in the past when priests on both sides of this argument still sent a piece of the Eucharist (the Fermentum) to each other. Irenaeus also looked at the early example of St. Polycarp and Pope Anicetus: 

And when the blessed Polycarp was at Rome in the time of Anicetus and they disagreed a little about certain other things, they immediately made peace with one another, not caring to quarrel over this matter…But though matters were in this shape, they communed together, and Anicetus conceded the administration of the Eucharist [Fermentum] in the church to Polycarp, manifestly as a mark of respect. And they parted from each other in peace, both those who observed, and those who did not [the common date of Easter], maintaining the peace of the whole Church (Eusebius, Church History, 5.24).

Obviously, this practice did not last up to our day, but the mingling of a piece of the host into the chalice did. While it no longer is a concrete sign of the union of the local Church, it still could be seen as a sign of unity both of the entire Church itself and of the Sacrament of the Body and Blood of Christ.

Unity, as a manifestation of Communion, comes in many forms.