This verse, along with the surrounding verses in Luke 3:23-38, forms the genealogy of Jesus, tracing his lineage all the way back to Adam. This specific section highlights a portion of that genealogy, naming a series of ancestors:

Methuselah: Famous for being the oldest person in the Bible, living to be 969 years old (Genesis 5:27).
Enoch: A righteous man who "walked with God" and was taken directly to heaven without experiencing death (Genesis 5:24).
Jared: The father of Enoch (Genesis 5:18-20).
Mahalaleel: The father of Jared (Genesis 5:15-17).
Cainan: The father of Mahalaleel (Genesis 5:12-14).

Significance:

Establishing Jesus' Humanity: The genealogy emphasizes that Jesus was a real human being with a traceable lineage. By connecting him to these figures from the Hebrew Bible, Luke grounds Jesus in human history.
Connecting to the Old Testament: The genealogy links Jesus to the Old Testament narrative and the history of the Jewish people. This is important because Jesus is presented as the fulfillment of Old Testament prophecies and the Messiah promised to the Jewish people.
Universal Scope: By tracing the lineage all the way back to Adam (Luke 3:38), Luke suggests that Jesus' salvation is for all humanity, not just the Jewish people. Adam is considered the father of all humankind.
Reliability and Accuracy: While some details of the Old Testament genealogies are debated by scholars, Luke's inclusion suggests he considered them important and reliable historical information.
Claiming Kingship: Genealogies were important in Jewish culture for establishing inheritance and lineage, including claims to kingship. Luke's genealogy aims to demonstrate Jesus's lineage from David, as promised in the Old Testament, to establish his right to be considered the Messiah and King of the Jews.

In short, this verse is a small piece of a larger genealogical narrative that serves to validate Jesus's identity, connect him to Jewish history and the Old Testament, and emphasize the universal scope of his mission.