Wikipedia says this about the Manchin-Toomey Amendment:
The Manchin-Toomey Amendment was a bi-partisan piece of legislation that would require background checks on most private party firearm sales, sponsored by Democratic Sen. Joe Manchin and Republican Sen. Pat Toomey. The amendment, S.Amdt. 715 to S. 649, was voted on and defeated on April 17, 2013 by a vote of 54–46. It needed 60 votes to pass.
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What law was this actually amending? Why did it need 60 votes to pass?
The Manchin-Toomey Amendment was an amendment to S. 649 - Safe Communities, Safe Schools Act of 2013, a bill which contained a number of limited gun control and school safety measures:
Safe Communities, Safe Schools Act of 2013 - Amends the NICS Improvement Amendments Act of 2007 (NICS Act), the Brady Handgun Violence Prevention Act (Brady Act), the Omnibus Crime Control and Safe Streets Act of 1968, and the federal criminal code to require background checks for all firearm sales, prohibit straw purchases of firearms, and expand the school safety grant program
The amendment needed 60 votes to be adopted because in the US Senate, the filibuster has become so common that nearly any business must overcome the 60 vote threshold needed to forcibly cut off debate on an issue.
You can read more about the filibuster here: https://politics.stackexchange.com/a/36090/19301
