Here Honorius describes the people’s offertory as it still existed in the 12th century
Some of the people sacrifice gold, some sacrifice silver, and some sacrifice from another substance. The priest and ministers immolate bread and wine with water. Those who offer gold signify the magi who brought gold to the Lord. Those who offer silver signify those who put money in the Temple treasury. Those who sacrifice from other substances are those who sent the Lord basic necessities, which Judas carried. They are those who sent their oblations to Jerusalem through the apostles Paul and Barnabas. Those who offer bread are those who pour out their spirit in a sacrifice of praise to the Lord. Those who offer wine are those who lay down their lives for their brothers. Those who offer water are they who hand over their body to be tortured for Christ.
Note the ascending hierarchical order of the gifts: pagans offering money, Jews offering alms, disciples offering Christ the necessities of life, Christians offering charity, and finally the sacrifice of the martyr. This is a beautiful compendium of the theology of sacrifice, understood as moving from the imperfect types of natural religion through the transitory epoch of the Jews toward its perfection in Christ and the martyr.
According to Jungmann, the people’s offertory took place in various ways in various places:
“In the ancient Milanese and Roman liturgies, and probably also in the North African, the offering of the faithful was very closely bound up with the eucharistic sacrifice. From the last of these, the North African liturgy, we get our oldest accounts of the offering of the faithful, and the customs connected with it are quite fully expounded, especially in St Augustine. In African it was possible to bring one’s offerings to the altar day after day, as Monica was wont to do. […] Thus the offering and the oblation of the gifts was built into the very structure of the Mass. […]
How the offertory was conducted at the papal stational service in seventh century Rome Rome, we know in fullest detail. Here the gifts were not brought by the people to the altar, but were collected by the celebrant and his retinue. After the Gospel the pope and his assistants first approached the nobility and received from them, according to their rank, their offerings of bread, while the archdeacon who followed accepted the wine (which was presented in special flasks or cruets and poured it into a large chalice…) […]
In other churches of the West, and more especially in the Roman liturgy after it was transplanted to Frankish countries, the oblation was metamorphosed into an offertory procession of the faithful. After the Credo a line was formed, which wended its way to the altar. First came the men, then the women; the priests and deacons joined in after them, with the archdeacon bringing up the rear. Frankish interpreters compared the procession to the parade of the multitude that went out to meet and acclaim our Lord on Palm Sunday. (Amalarius 813-814) (De eccl. Off. III, 19; Mitrale, III, 5.). Here, too, bread and wine form the offertory gift of the faithful. The English synod of Cealychythe (Chelsea 787) stresses the prescription that the offering should be bread, not cake. As a rule the bread was carried to the altar in a little white cloth; but mention is made also of woven baskets. The celebrant and his assistants went down to meet the offerers at the spot dictated by custom. We learn that the gifts were placed on a large paten carried by an acolyte. But even when they were offered up at the altar they were no longer set down on the altar itself, but post altare. For even when they still consisted of bread and wine, they were no longer intended for consecration. […]
Granting the principle that, besides the Eucharist, material gifts also could be presented to God, it was not long before the offerings consisted of objects other than bread and wine. […] Among the objects meriting the honor of being allowed to be brought to the altar, there appear, in addition to the oil for the lamps, especially wax and candles. Even at the present time, during the Mass of ordination, the newly ordained bring the bishop the newly ordained a lighted candle, which is presented to him. […] Even the transfer of immovable property was often executed by handing over a deed or voucher at the offertory. From the eleventh century on, the offering of money began to come to the fore. […] So since the twelfth century, in explaining the offertory, the enumeration of offerings usually begins with gold (Mitrale III, 5, Durandus IV, 30, 34.”
The old rites of canonization included an offering of candles, bread, and other items to the Pope, as shown in the images above and below, and explained in an excellent post on New Liturgical Movement.