Besides serving as a substitute in trades, money's other important use is as a store of wealth. In a straight barter system, the commodities being traded are generally perishable. You can gather tons and tons of wheat by making shrewd trade deals, but if you try to save the wheat, it will eventually go bad. Money allows people to accumulate wealth.
This had an enormous impact on civilization, because it meant that power wouldn't always be passed through families. People who had been excluded from any possibility of holding political power could amass wealth through trade or by providing a service. That wealth could then be used to purchase political or even military power. So money made civilization more democratic by taking some power out of the hands of noble families that had monopolized it for hundreds of years.