That section of the Youth Catechism for the Catholic Church explains itself quite clearly.
The quote you reference is the first line of the answer to the question:
With Jesus Christ, has everything been said, or does revelation continue even after him?
Including your quote, the answer continues on:
In Jesus Christ, God himself came to earth. He is God's last Word. By listening to him, all men of all times can know who God is and what is necessary for their salvation.
With the Gospel of Jesus Christ, the Revelation of God is perfect and complete. To make it comprehensible to us, the Holy Spirit leads us ever deeper into the truth. God's light breaks so forcefully into the lives of many individuals that they "see the heavens opened" (Acts 7:56). That is how the great place of pilgrimage such as Guadalupe in Mexico or Lourdes in France came about. The "private revelations" of visionaries cannot improve on the Gospel of Jesus Christ. No one is obliged to believe in them. But they can help us understand the Gospel better. Their authenticity is tested by the Church.
So it says, in the first paragraph, that the Gospel (good news) of Jesus Christ is Universal in scope - valid for "all men of all times" and Ultimate in purpose - they "can know who God is and what is necessary for their salvation." It goes on to imply, in the second paragraph, that it is possible to receive additional "private revelations", but they will only be judged authentic if they are consistent (and don't go 'beyond') the 'final' (in terms of completeness or what is required - "perfect and complete" - not final in a temporal sense) revelation that God has given us in Christ. It is the Church that can make the determination of whether "private revelations" are in accord or contradictory to the 'final word'.
It then further explains the important concept of:
Incarnation - from the latin caro, carnis=flesh, "becoming flesh". God's act of becoming man in Jesus Christ. This is the foundation of Christian faith and of hope for the redemption of mankind (emphasis added)
i.e. God speaks to us most clearly (and 'finally' in the sense given before) by becoming one of us, and yet showing his Holy nature within the context of human flesh - "God himself came to earth".
It further references (part of) the scripture that most clearly delineates this doctrine:
1 In many and various ways God spoke of old to our fathers by the prophets; 2 but in these last days he has spoken to us by a Son - Hebrews 1:1-2a RSV
The quote stops there, but it is well worth examining the complete discourse on the topic at the beginning of the epistle to the Hebrews which actually continues well into the third chapter: Heb 1:1-3:6 RSV, with further illumination on the superiority of Christ over all servants of God later in the epistle as well.
Finally, it includes illuminating quotes from the Catholic luminaries Blaise Pascal:
Apart from Jesus Christ, we do not know what God, life, death, and we ourselves are
and Mother Teresa of Calcutta:
I have no imagination. I cannot picture God the Father. All that I can see is Jesus.
These quotes are in line with the Bible's teaching from 1 John 4:12-15 & 20 RSV:
12 No man has ever seen God; if we love one another, God abides in us and his love is perfected in us. 13 By this we know that we abide in him and he in us, because he has given us of his own Spirit. 14 And we have seen and testify that the Father has sent his Son as the Savior of the world. 15 Whoever confesses that Jesus is the Son of God, God abides in him, and he in God... 20 If any one says, "I love God," and hates his brother, he is a liar; for he who does not love his brother whom he has seen, cannot love God whom he has not seen.
Additionally, not mentioned in that particular section, is the concept of Jesus as the 'logos' i.e. the eternal word of God (cf. John 1). In this sense, Jesus is the first and last word of God and every word in between! For example:
10 The prophets who prophesied of the grace that was to be yours searched and inquired about this salvation; 11 they inquired what person or time was indicated by the Spirit of Christ within them when predicting the sufferings of Christ and the subsequent glory. - 1 Peter 1:10-11 RSV (emphasis added)
Summary: Jesus is God's 'last word' in the sense that through Him and only Him can we truly know God - any others that have or teach a contradictory revelation are respectively deceived or deceivers.