A Levi is a Levite, that is, a descendant of Jacobs third son. Levites often have surnames attesting to their lineage such as Levy, Levin, Leventhal etc.
Levites today have two main privileges. One is being called up second to the Torah (after the Cohen). The second is to wash the hands of the Cohanim before the latter go up to bless the people.
This second task harks back to their Temple role. As well as serving the priests there, they also played music and sang in the Temple services. This special role in the service of the sanctuary originated after the Sin of the Golden Calf. The Torah records that the Levites didnt take part but instead answered Moses call for loyalty: Whoever is for the Lord, come here! (Exodus 32:26).
The word Levi itself means to join or be connected. It can also be to assume an obligation. The word for a borrower is loveh. A funeral is a levayah, when mourners accompany the body to the grave. A livui neshek in modern Hebrew is an armed escort.
Jacobs son, Levi, was so called by his mother Leah, recording the ups and downs of the struggle with her sister and co-wife Rachel for Jacobs affections. When Levi is born she says, This time my husband will become attached (Yelaveni) to me for I have born him three sons.