The unit of analysis is the major entity that is being in a study. It is the 'what' or 'who' that is being studied. In social science research, typical units of analysis include individuals (most common), groups, social organizations and social artifacts.
The literature of international relations provides a good example of units of analysis. In "Man, the State and War", Kenneth N. Waltz creates a tripartite analysis with three different units of analysis: the man (individual), the state (a group), and the international system (the system in which groups interact).
This is not to be confused with the unit of observation, which is the unit described by one's data (neighborhoods using the U.S. Census, individuals using surveys, etc.). For example, a study may have a unit of observation at the individual level but may have the unit of analysis at the neighborhood level, drawing conclusions on neighborhood characteristics from data collected from individuals.