What is happening here
Between the First Reading and the Second Reading, the assembly responds in song with a psalm. The Responsorial Psalm is not a second reading; it is the people's response to the Word they have just heard, given in the very prayers that Christ himself prayed in his earthly life and that the Church prays without ceasing in the Liturgy of the Hours.
The structure is simple. A cantor or psalmist sings the verses; the assembly sings the antiphon (the recurring refrain) in response. The antiphon is usually drawn from the psalm itself or from the day's Gospel, and it captures in a single line the spiritual heart of what the assembly is being asked to make its own.
The Responsorial Psalm is properly sung, not recited. The General Instruction of the Roman Missal is direct on this point: "the responsorial psalm should as a rule be sung." The reason is that the psalms themselves are songs — they were written to be sung, prayed in temple worship, prayed by Jesus, prayed by every monastic community since the early Church. To recite a psalm is possible but always second-best.
For Catholic weddings, the Responsorial Psalm is one of the most beloved choices a couple makes — Psalm 128 ("Blessed are those who fear the Lord") and Psalm 34 ("Taste and see the goodness of the Lord") are among the most commonly chosen. For funerals, Psalm 23 ("The Lord is my shepherd") is the universal favorite. The choice of psalm shapes the sound and feel of the entire liturgy.