While the census does use geographies we are all familiar with such as states, counties and places (e.g. cities), it also uses geographies very specific to the census. Smaller area geographies with locally designated boundaries, such as community planning areas and neighborhoods, are not used in the census. Rather, the census uses specialized geographies that allow for a standardized way of looking at areas smaller than a city. Various census data is available for a number of geographies, but the ones below are generally the easiest for breaking down a city or county into more manageable and/or relevant sections.
Census Block: This is the smallest unit of census geography. A block generally corresponds to what we would think of as a city block, bounded on four sides by streets. Depending on the area, other boundaries may be used to define as block, such as railroad tracks, water, and even power lines in some rural areas. Blocks tend to be the most stable of the small census geographies, as population numbers are not generally used to define them. Only 100 percent data is tabulated at this level, as the population numbers are too small to tabulate sample data and still ensure respondent anonymity.
Census Block Group: A collection of blocks, a block group is the smallest geography for which sample data is tabulated. An ideal block group has a population of 1,500 people, with populations ranging from 300 to 3000 people.
Census Tract: Although census tracts are designed to be relatively stable statistical subdivisions of a county, they may change between censuses because they are roughly based on population numbers. The ideal population of a census tract is 4,000 people, but they may vary between 1,000 and 8,000 people. Although the tracts may change between censuses, an effort is made to keep the areas comparable. For instance, a tract that had large population growth in the 1990 census may have been split into two tracts for the 2000 census, but those two tracts together retain the same boundaries as the original 1990 tract to allow a direct statistical comparison of the areas.
Zip Code Tabulation Area (ZCTA): This geographic area is roughly equivalent to the U.S. Postal Service zip code areas (both 3 and 5 digit) we are all familiar with. Since zip codes do not always line up with census-defined blocks, ZCTAs were created in order to allow tabulation of data for zip code areas. A census block is placed in the ZCTA that corresponds to the majority of zip codes assigned to addresses in that block. As a result, a ZCTA may not include all houses that receive mail in that zip code, but it is the best equivalent available.
A note on confidentiality: because of the personal and sometimes sensitive nature of the information collected for the census, the Census Bureau strives to maintain a high level of confidentiality to help ensure that an individual person or household can't be identified via the published data. This concern is greatest, obviously, for smaller geographic areas like blocks or even tracts. Be sure to pay attention to footnotes/documentation when reviewing data for these smaller areas, as you may find important details about how the reported data may have been affected by confidentiality protections.
'Census Small-Area Geography' graphic from the U.S. Census Bureau.