That statement is not really accurate. Nixon ended fixed dollar-gold convertibility in 1971. You are probably thinking of FDR' nationalization of gold reserves, which isn't really "ending the gold standard." Initially, under Bretton Woods, the US dollar (and by extension, pretty much every other Western country's currency) was pegged to gold. Once the US no longer had enough gold to be able to maintain international confidence in the peg, and a "gold run" became a possibility, the system was abandoned.
The US still maintains a gold reserve to preserve confidence in the dollar, but we don't know for sure how large these reserves actually are because the US government has refused to allow a full, independent audit.