Once the bread and wine are consecrated at Mass they are changed from physical food into Jesus Christ. The best way we can describe this is transubstantiation, but this is no more than a description, not a scientific proof. It is a mystery and a priceless gift. Consequently, all kinds of customs have grown up around the Eucharist.
Have you ever noticed what the deacon or priest does to the flagon of wine once it’s brought forward at the Offertory Procession? Before he pours it into the chalices he pours a small amount of water into it, usually no more than a half-tablespoon. Why? In ancient times common wine was strong, thick and rather harsh. People routinely diluted it with water to soften the taste and to make it go further. That was why the priest added water; it was a routine procedure that was considered good manners. As the monasteries began planting their own vineyards and making better quality wines it was no longer necessary to dilute it as much, but the habit remained and so, to this very day, we add a token amount of water because “that’s how we’ve always done it.” Some people like to explain it as a symbol. They say think of humanity as the water and of the wine as representing Jesus. We (the water) are poured into Jesus and disappear into Him — He makes us one with Himself. That’s a beautiful image, don’t you think?
Now, why does the priest break off a small portion of the large host and drop it into the chalice during the Agnus Dei (Lamb of God)? Again, we have to go back to the ancient church. Every Sunday when the pope said Mass he’d break off pieces from the bread he had consecrated and a deacon would take one of the pieces to each of the other churches in Rome; this represented that every priest saying Mass was “in communion with” the chief of the apostles, the pope. Some bishops began following that example in their own dioceses. Ultimately, there were so many churches with so many Masses that the custom could no longer be continued, but the priest celebrating the Mass would break off a portion as a reminder to himself and the congregation that they were a part of the greater church. We are Catholic because we maintain our relationship with the apostles and their successors, united under the leadership of the pope, the successor of St. Peter.