Reserve status is self-reinforcing. Deep government bond markets and open capital accounts make a currency worth holding; holdings make it the natural invoicing and settlement unit; that in turn creates the demand for it as a vehicle described in dollar-pair and the offshore lending market in eurodollar-market.
The dollar has accounted for roughly three fifths of disclosed official reserves in recent decades, with the euro a distant second and the yen, sterling and others sharing the remainder. Shifts happen over decades, not quarters.
The practical consequence for traders is that dollar funding conditions transmit worldwide. When dollars become scarce, the currency strengthens against almost everything at once regardless of US fundamentals, a pattern described in dollar-smile and mitigated by a central-bank-swap-line.
Example: a Brazilian importer buying from a Korean supplier may settle in dollars even though neither party is American, requiring two conversions and creating dollar demand that has nothing to do with the US economy.
Related: eurodollar-market, dollar-pair, central-bank-swap-line, fx-reserves