Essentially urban populations were decimated, which led to a few major changes.
To summarize/ TL;DR The Black Death killed many people and resulted in the rise of nobles who profited more from labor shortages than from their family titles. On a more psychological level, it appears that Medieval people saw the Black Death as divine judgement for their sins, and tried to reform their piety accordingly.
I can only speak from my research on a post-Black Death Sienese votive panel painting that's at my school's art museum, so if you want I can indirectly answer your question with a case study.
Northern Italian city states were unique phenomena of the Late Middle Ages. While the nobility still gained most of their wealth through titles and estates, and craftsmen were still greatly burdened by the limitations of guilds and workshops, populations managed to amass around commercial centers/transportation hubs that had access to the Mediterranean trade network. Because of the nature of Medieval society, wealthy landowners became the leading citizens of these cities. Their patronage of buildings and infrastructure within cities led to the creative outpouring that we associate with the Italian Renaissance.
Siena, one of the cultural epicenters of the Late Middle Ages in Italy, produced many prolific painters in the early 14th century. These included Duccio, Segna di Bonaventura, the Lorenzetti Brothers, and Simone Martini. Duccio's [Maesta altarpiece created for the cathedral of Siena in the 1310s](http://en.wikipedia.org/wiki/Maestà_(Duccio), for example, was one of the most revered and influential paintings of the pre-Renaissance period.
However, these painters were all hired by the urban elite of Siena to decorate new urban infrastructure. Duccio's Maesta, for example, was made specifically for the leading citizens of Siena who wanted to glorify the cathedral that they had patronized. The painting also figured prominently in public ceremonies, festivals, and processions, due to its almost talismanic association with warding off bad luck.
Much of my research was based on Judith B. Steinhoff's Sienese Painting After the Black Death. To summarize her argument, the Black Death killed off many lower-class workers, many workshop masters such as the painters listed above, and many urban elites who funded much of the construction and public ceremonies in Siena.
She argues that:
Faced with pressing problems of population, labor, and food shortages in the immediate wake of the plague, the Sienese government redirected many of the resources it had previously invested in art and architecture (70).
Steinhoff goes on to argue that
...particular kinds of subjects, namely narratives and donor portraits, were in greater demand…Many of these commissions reflect a change in values stemming from an intensified search for more personal forms of piety (71).
Hayden B. J. Maginnis, in his book The World of the Early Sienese Painter, also argues that after the Black Death in Siena "there was a societal reluctance to create monuments of self-commemoration” (148). This can in part be associated with the idea of 'civic piety' in Italian city states, where specific saints were adopted as figures to ward off bad luck. Maginnis argues that in painting after the Black Death, we see a disillusion with the effectiveness of these patron saints.
The panel painting at the AMAM that I did some research on was produced after the Black Death. It captures a few subtle changes in Sienese society:
The inclusion of a donor portrait (person kneeling on the bottom right) in the painting shows that it was created not for the city of Siena, but for the sole use of a single urban elite. This shows the disillusion with 'civic piety' after the Black Death, and how there was a preoccupation with 'self salvation'.
The donor is not depicted in French knightly armor, like most previous self-depictions of Sienese nobility, but in urban Italian clothes. This possibly indicates that the patron of this painting was one of the novo-rich who profited off of the annihilation of competition following the Black Death.
The excess of gold and the detailed representation of drapery show that the person who paid to have this painting made was very rich. This was a reality of post-plague Europe: people could take dead people's money and could be paid more for their services since there was less people to work.