This verse is a genealogical listing from the book of Nehemiah. It's essentially a family tree. Let's break it down:

"Of the Levites:" This indicates that the person being introduced, Shemaiah, belongs to the tribe of Levi. The Levites were a tribe within Israel designated for religious service, particularly in the temple.

"Shemaiah the son of Hasshub, the son of Azrikam, the son of Hashabiah, the son of Bunni;" This is the lineage. It shows Shemaiah's direct male ancestors:
Shemaiah is the son of Hasshub.
Hasshub is the son of Azrikam.
Azrikam is the son of Hashabiah.
Hashabiah is the son of Bunni.

Therefore, the verse simply identifies Shemaiah as a Levite and traces his ancestry back four generations.

Why is this included in Nehemiah?

Genealogies are common in the Bible, particularly in books like Nehemiah, Ezra, and Chronicles, which deal with the rebuilding of Jerusalem and the re-establishment of Jewish religious life after the Babylonian exile. These lists served several important purposes:

To establish lineage and identity: In a time of rebuilding, knowing who belonged to which tribe and family was crucial for determining roles and responsibilities, especially for the Levites and priests.
To verify legitimate claims to positions: Being able to trace ancestry back to specific figures was important for claiming rights or privileges, especially within the priesthood or Levites.
To preserve the memory of the people: These lists helped to maintain the collective memory and identity of the Jewish people, ensuring that their history was not lost.
To demonstrate God's faithfulness: By showing the continuity of families and the fulfillment of God's promises to preserve a remnant, these genealogies demonstrated God's faithfulness to His people.

In summary, this verse is a small piece of a larger effort to document and re-establish the Jewish community after the exile, emphasizing the importance of lineage and identity within the tribe of Levi.