Most statistical methods require samples. If an economist wishes to use any statistical method that has this requirement, including commonly used methods such as ANOVA (for analyzing how groups vary), null hypothesis testing (for testing whether there are differences between groups) or regression analysis (for making predictions), he must take a sample. These methods, being created with mathematics, have the assumption that we are looking at a random subset of a population.
While it would be ideal to have access to all information of a certain type of company, product or consumer, this is impossible in the real world. In a situation which economists wish to compile information on a certain subject of considerable complexity or breadth, the only reasonable way to do so is to use a sample from the population. In this way, economists can place upper limits on the time and money spent on compiling this information.
Some problems in economics are complex to the point that strong theories cannot come straight from individual thoughts. To gain understanding of the phenomenon of interest, economists look at companies and consumers to observe their roles in the phenomenon. After gaining sufficient information, economists can begin to develop theories on these phenomena.
Samples allow economists access to the real economic world in a way that allows them to observe how real-world economics and theoretical economics match (or mismatch). After creating a theory, an economist takes a sample from a population to gather evidence for his theory. Without samples, all supporting evidence for his theory would be considered subjective.