What are some benefits of using a sample instead of a census?
The primary benefit of using a sample rather than a census is efficiency. Suppose that someone wants to know what the average opinion of Congress is among individuals 18-24 (i.e., they want to know what Congress's approval rating is among this demographic). In 2010, there were over 30 million individuals in that age range located within the United States, according to the US census.
Going to each of these 30 million people and asking their opinion, while it would certainly lead to very accurate results (assuming no one lied), would be tremendously expensive in terms of time and resources. Further, given that any single individual's personal response will have a very small impact on the overall result, one would get a very poor return on the investment of resources into gathering this census.
However, using a truly random and appropriately sized sample can enable one to approximate the desired data to within an acceptable margin of error, while drastically reducing the time and resource expenditures. Thus, the individual above may wish to choose a random sample of 10,000 individuals, or perhaps 100 from each congressional district. It must be emphasized, however, that a non-random sample may very likely lead to a drastic difference between the sample statistic and the population parameter.
As an example, suppose that the individual above chooses 500 people between the ages of 18 and 24 in each state from a list of registered Democrats. Given that the political affiliation of those surveyed may lead to their responses different from those provided by the "average" member of the population, this sample could be said to be biased, and thus not an accurate representation of the population as a whole.