What does the expiration date of current non-immigrant status mean?

The expiration of " status" is the expiration of the stay authorized by CBP at the port of entry or by USCIS in the case of an extension of status as reflected in the FORM I-94.

After the date a visa is expired, you can no longer use it to be admitted into the U.S.

Depends on whether you are inside the USA or seeking to enter the USA on a visa in your passport. If inside the USA, that does NOT mean the expiration of your "visa", but of your I-94. Once the date of your current NIV status has expired, you start accruing "unlawful presence" - 180 days or more and you'll be triggering the 3 year inadmissibility bar once you depart, and 365 days = 10 year bar.

Non-immigrant stay – I-94. .