With her third son, Leah reaches for a new hope. This time, she thinks, Jacob will at last be yilaveh — attached — to her (Genesis 29:34). So she names the child Levi, from the root meaning "joined."
The Targum Pseudo-Jonathan hears a second meaning the moment the name is spoken. Thus will it be that my children shall be united to serve before the Lord.
Leah's personal loneliness is reinterpreted as a prophecy of spiritual attachment. She wanted to be joined to her husband. The Holy One hears her and says: your tribe will be joined to Me.
Levi will become the tribe of the priesthood. Aaron and Moses will descend from Levi. The Levites will carry the Tabernacle through the desert. They will stand in the Temple courts to sing the daily psalms. They will be the one tribe without a land inheritance, because their inheritance is the service of God Himself (Numbers 18:20).
Leah was asking for a husband who would be present. God gave her a tribe that would be present in the Sanctuary. The attachment she could not secure in her marriage became the attachment of an entire tribe to the altar.
There is tragic beauty in this. The woman whose husband would not stay in her tent becomes the mother of the only tribe that lives permanently inside God's tent. The Levites never leave. The Mishkan (Tabernacle) and the Beit HaMikdash (Temple) become, for Leah's line, what Jacob's love was not.
The takeaway: the attachments we cannot receive in our own lives sometimes become the destiny of our descendants. Leah's unfulfilled longing became the priesthood of Israel.