Ruth 1:2

וְשֵׁ֣ם הָאִ֣ישׁ אֱֽלִימֶ֡לֶךְ וְשֵׁם֩ אִשְׁתּ֙וֹ נָעֳמִ֜י וְשֵׁ֥ם שְׁנֵֽי־בָנָ֣יו׀ מַחְל֤וֹן וְכִלְיוֹן֙ אֶפְרָתִ֔ים מִבֵּ֥ית לֶ֖חֶם יְהוּדָ֑ה וַיָּבֹ֥אוּ שְׂדֵי־מוֹאָ֖ב וַיִּֽהְיוּ־שָֽׁם׃

Translation: Now the name of the man was Elimelech, and the name of his wife was Naomi, and the names of his two sons were Mahlon and Chilion: Ephrathites from Bethlehem in Judah, and they came to the fields of Moab, and they remained there.

Notice that the verse begins with vav + noun. This is an indicator that we now have an explanatory comment off the main line of the narrative (the main line of the narrative being carried by the vav-consecutive + imperfect). The narrative then picks up again with (וַיָּבֹ֥אוּ). This explanatory comment gives us the names and place of origin of these people. Some commentators want to make something out of the names, noting, for example, that “Elimelech” means “my God is king.” However, the etymology and thus the meanings of the names of Mahlon and Chilion are uncertain, and the only name that is given particular attention is “Naomi,” and that is later in the narrative. At this point in the story, the author has simply identified the characters for us.

The use of (וַיִּֽהְיוּ) may seem unusual for the beginning student, but see BDB III.3 for the use of (הָיָה) for remaining in a place.

The main line of the narrative so far tells us that in the time of the judges, there was a famine in Israel. A certain man from Bethlehem sets off to Moab, arrives there, and settles there. Additional explanatory information tells us that the man did not go alone, but rather took his wife and sons, who are then named.