In simplest terms, a census is a count of all persons in a given geographic area. The United States Census Bureau conducts a census every 10 years, as mandated by the U.S. Constitution. The data from those counts is used to determine the number of seats each state has in the House of Representatives and to guide the distribution of federal funds to local communities.
The first U.S. census was held in 1790 and counted only heads of household. Over time, the census has evolved to count every person in the U.S., including information on their age, race, ethnicity and more. The census is designed to count all people (regardless of immigration status) living in the U.S. at the time of the census and is the closest we have to complete demographic and economic data on the U.S. population. It is important to understand, however, that there are usually segments of the population that are over- or under-counted for a variety of reasons.
Census questions may change from census to census, sometimes dramatically, which means that the statistics available also change. The easiest way to find out what information is available for a specific census is to look at the questionnaires. If the question wasn’t asked, the data isn’t available. Original questionnaires and instructions for each decennial census are available on the Census Bureau's website. The Bureau's publication Measuring America: The Decennial Censuses from 1790 to 2000 provides lots of additional details.
Between 1970 and 2000, the decennial census included a “short form” with questions asked of every household in the country, as well as a “long form” answered by about 1 in 6 households. Questions on the short form (age, race, etc.) are the basis for the census 100% data. Questions on the long form (education, income, etc.) were the basis for the census sample data or estimates. Beginning with the 2010 census, the long form was discontinued; instead, sample data previously collected on the long form is now collected regularly through the American Community Survey (ACS).
The first two resources below are the most comprehensive collections of decennial census/ACS statistics for general users. Social Explorer, which is restricted to UCSD affiliates, is easier to use than data.census.gov and includes historical data. Data.census.gov, a product of the Census Bureau, is freely available on the web.
Most references to "the census" pertain to the decennial census and the American Community Survey. In addition to these, the Census Bureau conducts many other surveys and programs, including the Economic Census and Census of Governments. The Bureau also provides a number of data tools to help find statistics from their surveys, including the Census Survey Explorer that helps you find the best/right survey by filtering and searching by geography, frequency, topics, and subtopics. There is also a Census of Agriculture, which is conducted by the Department of Agriculture.
The Finding Data & Statistics guide can help you locate additional sources of Census and related data. See especially the Find Data by Topic tab, which includes pages for People: Demographics & Population, People: Race & Ethnicity, San Diego & California, and more. Many of the resources are restricted to UC San Diego users.