Some quotes from this article:
Where do preferences
originate? How are they formed? How does the economic, social, legal, and cultural
environment shape the formation of preferences? In recent years concepts such as ‘habit
formation,’ ‘social norms,’ ‘cultural values,’ ‘conspicuous consumption,’ and others have
been formalized in various ways in the economics literature in an attempt to begin to
answer these difficult questions. Yet, mainstream economic theory typically assumes that
preferences are exogenous and stable. [...] economists should take them as given and analyze the implications for economic behavior (Friedman, 1962).
The endogeneity of preferences implies that not only individual preferences [...] determine
economic outcomes, but also that the economic, social, legal, and cultural structure of society affects
preferences.
Thus, using endogenous preferences allow a researcher to study phenomena where social interaction (e.g. networks, influence, marketing, etc) is relevant for consumption choices. For example, here is a paper studying "fashion cycles". Preferences for individual $i$ are quite simply define as Cobb-Douglas functions:
$$ U^i = x^{\alpha_i} y^{1-\alpha_i} $$
where $x$ and $y$ are two goods, and $\alpha_i \in (0,1)$. Preferences are endogenised by assuming that $\alpha_i$ depends on society's past level of consumption of good $x$. Therefore, how much other individual have consumed in the past affects how much an individual would like to consume today. In this sense, preferences are endogenous. This contrast with common exogenous preferences where individual choices do not depend on other individual choices (other than through common market mechanisms like price, demand-supply).
This article offers a brief history of exogenous preferences.