The person speaking was teaching that Psalm 23 is the Psalm that the early Christians would recite on the way to the Easter Vigil (and probably during) when new members were welcomed into the Church.
Being welcomed into Holy Mother Church means receiving the three Sacraments of Initiation; Baptism, the Eucharist and Confirmation.
Let's go through the Psalm and break it down:
"The Lord is my shepherd, I lack nothing.
2 He makes me lie down in green pastures,
he leads me beside quiet waters,
3 he refreshes my soul." (Psalm 23: 1-3)
The quiet waters are the waters of Baptism, which remove our original sin as infants and all sins up to that point as adults, and bring us into God's family.
"You prepare a table before me
in the presence of my enemies." (Psalm 23:5)
The table He spreads for us is the table of the Eucharist where Jesus feeds us with His own Precious Body and Blood.
"You anoint my head with oil;
my cup overflows." (Psalm 23:5)
The oil used at Confirmation is called Holy Chrism and "is a mixture of olive oil and balsam," and is used to signify favor and strength from the Lord. (Catholic Education Resource.)
All of these Sacraments bring us into the Church which leads us to our final resting place with Jesus in heaven.