What does being Born Again mean per Catholic teaching?
Jesus answered and said to him, “Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God.” (John 3:3 NKJV)
No 1213 Catechism of the Catholic Church under THE SACRAMENT OF BAPTISM summarises what baptism is:
1213 Holy Baptism is the basis of the whole Christian life, the gateway to life in the Spirit (vitae spiritualis ianua) [4 Cf. Council Of Florence: DS 1314: vitae spiritualis ianua.], and the door which gives access to the other sacraments. Through Baptism we are freed from sin and reborn as sons of God; we become members of Christ, are incorporated into the Church and made sharers in her mission: "Baptism is the sacrament of regeneration through water in the word." [Roman Catechism II,2,5; Cf. Council Of Florence: DS 1314; CIC, cann. 204 § 1; 849; CCEO, can. 675 § 1.]
The answer to the question is in bold.