"How important were towns" is kind of a tough question to answer, because the existence/increase of towns is both a sign and a cause of overall exonomic restructuring over the later Middle Ages. Towns were essential to the economic system they were a part of/helped create. You can say something like by 1300, about 65% of England's economic production was shipped overseas, which meant it came through market towns, but obviously this was heavily agricultural/pastoral commodity. And of the 35% or so internal trade, that would be intimately bound up in a market/rural/urban web.

As Christopher Dyer neatly sums it up, by the late Middle Ages, tow key developments had happened. First, lords were thinking about economic productivity and how to get more out of their land. (But at the same time, we are in the days of the moral economy as well--fixing bread prices to make sure everyone can afford at least A Loaf of bread each day, even if it was a smaller load when grain prices rose). Second, the transition from crop to cash rents, which would be accelerated by the Great Famine in1315-1322, was already underway.

Thus, lords expected income in cash from their peasants, paid it in tax, and sold their share of crops on their land for cash. Day laborers in the countryside were paid in cash and needed somewhere to buy the necessary goods to stay alive. Conversion of crops to cash meant longer distance trade, which meant traders--and the people to support them. Who, in turn, produced more refined goods and services for each other, and maybe for rural dwellers who might spend more time gearing up for production of what brought them cash (either their own crops or as mill workers, harvest laborers, miners).Talking about towns is inseparable from talking about long-distance economies overall. (Since "national" can be a questionable term still at this time. Centralized/royal authority isn't even always an aspiration of rulers, much less a fact.)

But there are a couple of things we can look at to get a bit deeper. First, towns enabled specialization of profession--the ability to make a living from a very narrowly focused line of work which, overall, meant a greater variety of goods being produced in abundance. Secondly, towns were vital to economic growth.

Towns were signs and causes of specialization in profession. And medieval people could be very, very specific about what constituted a "profession." In Rouen, for example, the guilds for women (yes, women!) who made clothes out of new fabric versus those who made clothes out of secondhand fabric were not only separate but often at war in the courts for encroaching on each other's territory. Nuremberg had a dedicated craft (Nuremberg's formal guild system was abolished around 1348) of gingerbread baking.

The Nuremberg Hausbücher are a great example of how specialized professions could be. You can navigate around the site--I've sorted it by "profession" for you--and click through to see illustrations of the different jobs or people who did them in late medieval/early modern Germany.

http://www.nuernberger-hausbuecher.de/index.php?do=list&tt=prs-jobnorm

Probably the most important urban profession was not unique to towns, but it illustrates well the central role that towns played in economic development. In northwest Europe, it was increasingly popular for teenage men but especially women to move to cities and work as servants for a period of time, saving up money for marriage or to start a singlewoman's household. (The medieval demographic imbalance between women and men was heightened by the fact that a higher proportion of women moved to cities and stayed; a higher proportion of men stayed in or went back to the countryside.)

What Hajnal originally identified as the "European marriage pattern," of women and men both marrying later in northwest Europe connected to which countries' economies grew relatively stronger in the early modern era, isn't quite a marriage pattern. Women in Eastern Europe show a wide variety of ages at first marriage; even in Italy many women married later than we are often given to assume. Instead, it seems to be a women's wages pattern. Places with towns where women worked--acquiring cash income, spending cash income--generally speaking saw more economic growth from the late Middle Ages on.

I'm still struggling to say "how important were towns" because without them, the late medieval economy would have had to look completely different. This would have been true at the local level, the regional level, the "national" level, and the international level. But within the system that existed, specialized professions and their products would seem to be a good illustration of the economic contributions of cities to local life rather than just long-distance trade.

I am not a historian, but have studied a decent amount of economic geography and I think the "central place theory" may provide a theoretical explanation of the importance of small towns in the middle ages. The wikipedia article on central place theory provides a pretty decent breakdown of the important components, but I will provide some explanation of why I think it's relevant.

Agriculture provides an important foundation for all societies and economies. This is true today and it was true in the middle ages. Farms require relatively large plots of land with relatively few residential premises. The people who who farm the products on that land require non-farm goods and services as well as markets to sell their agricultural products. The distance between the farm and these service centres and markets has an impact on the efficiency of the farm/farmer. It takes time to cover distance, and in that time the farmer could be doing other things and at a certain point their produce will go bad if it takes too long to get to market. Towns naturally develop because they act as aggregation centres for agricultural production. Larger towns develop because they act as the next level of economic aggregation, and this pattern of increasing settlement size goes through iterations until you get cities. This is why there are loads of small towns relative to cities; the small towns can provide a number of lower-tier functions for local residents, and large urban centres provide regional functions for dozens of small towns and rural areas. Agriculture was certainly more important to the national economic system hundreds of years ago than it is today, so there is no doubt that those small towns were critical components of the national agricultural economy. I would imagine that towns also played a crucial role in defending the nation from intruders. It's much easier to defend your agricultural land if it's occupied than if you need to march an army across the country to push your foe back across the border. I gather that's why there are so many castles in the UK, but here I'm only speculating based on my pop-culture knowledge of medieval history.

Adam Smith, the "father of economics" provides a number of potentially relevant insights in his book the Wealth of Nations. I have not completed the book, but he essentially explains how an "economy" works from the ground up, and agriculture and distances between places play very important roles. The concepts he discusses kind of feed into the central place theory that I mentioned. He does mention that in the 1700s many of the jobs in small towns were also present in great towns, but the wages were almost always lower in the small town. This is primarily because rents are also lower, so the trade off between the two results in essentially a similar quality of life across space. I would assume that the case was similar in the middle ages because the book is very theoretical and the concepts still hold fairly consistent today. Obviously there would be unique instances of towns with specializations due to their geography, such as mining towns.

I don't know if I directly answered your question, but your question kind of pokes at some major theories in economic geography, so hopefully the things I mentioned are somewhat informative.

Follow on question for the OP - did the advent of modern last names arise with urbanization where first names would have required family last names?