It means that countries around the world tie their currency to United States dollar for valuation. What does this mean?
It means that in 1944, 44 nations gathered at a hotel in Brettonwoods New Hampshire and signed the Brettonwoods agreement. In this agreement, the nations agreed that the currencies around the world should be tied to something that had universal value. They decided that that universal thing would be gold.
At the time, the US held about 2/3 of the worlds gold. As a result, the 44 nations agreed that the US dollar would be tied to gold and all of these nations currencies would be tied to the US dollar.
When the United States terminated the convertibility of the US dollar to gold in 1971, the US dollar became Fiat money but still held its reserve status in countries around the world.
The clearest example of this is the petrodollar. Countries around the world have been forced to buy all of their oil in US dollars. Basically they have to convert their currency into US dollars and buy the oil. This is why the US dollar is considered the world reserve currency.