How did the revival of trade and cities during the High Middle Ages impact European society as a whole?
There were many impacts that came about because of this revival. Let us look at two of the most important.
First, there was the start of capitalism and a money economy. This was not fully developed yet, but it was beginning. The money economy was coming to replace barter as it was much easier to use money for all of the trading that now needed to be done. This led to the creation of banks and of trading companies where there were people whose livelihood came not from making goods but from buying and selling them. This can be seen as the start of capitalism.
Second, there was a move away from feudalism and towards a system of towns that had their own rights outside of that system. Trade and towns were not really compatible with the old system of feudal lords with serfs and peasants tied to the land. Therefore, towns started to be granted charters of their own and the right to exist outside the feudal system. The feudal system was still strong, but this growth in trade and cities was starting to diminish its power.
Trade in the High Middle Ages came from several major events in world history; let's focus on the Black Death and the Crusades.
From 1347-1351, the Black Death travelled across the Asian Steppes and found its way into Sicily from Italian merchant ships trading across the Black Sea. The plague was devastating for Europe; most estimates place the death toll at about 1/3 of Europe's population. One of the biggest social impacts the plague had on feudal manors was that it killed off a majority of peasants in some regions. With less labor to keep the fields productive and tilled, the peasants were overburdened with work and demanded more rights. The economy suffered and Europe looked more heavily into trade. Guilds formed to train more people in crafts and artisanry, and coupled with banking systems and networks like the Hanseatic League in northern Germany, trade became a stronger part of Middle Ages economies.
The Crusades was a period of time when Catholics sought to reestablish holy land in/near Jerusalem. While this didn't pan out as planned, one of the biggest successes to come out of the Crusades was the reintroduction of Eastern trade, goods, philosophies, and thought in Europe. With the influx of new information, technology, and ideas, Europe's economies benefitted from this renewed trade.
While feudal systems stayed in place for a while after the reintroduction of trade with the East, the West definitely benefitted from the growth of a modern banking system.