This means that the people you see around you in the pews are important, but it goes further. We also receive the prayers, encouragement, and support of the unseen hosts of heaven. In the Liturgy of the Word, God speaks to us through the inspired words of the prophets and apostles. In the Liturgy of the Eucharist, the whole company of saints and angels are present with us, worshiping our Lord together. The saints and angels are specifically mentioned in the Eucharistic prayers to highlight this reality.
The communion of saints is Christ's Body, so closeness with him implies closeness with our brothers and sisters. As the Catechism says, “Since receiving this sacrament strengthens the bonds of charity between the communicant and Christ, it also reinforces the unity of the Church as the Mystical Body of Christ" (1416).