Data visualization is a way to present data in a graphical or illustrative format to allow for greater comprehension of the concepts you're trying to demonstrate. Visualizations can be simple like pie charts and timelines, or complex, multivariate, and interactive.
A multitude of examples of data visualization can be found on A Periodic Table of Visualization Methods.
Data Visualization has two primary purposes: Analysis and Communication
For an example of how different four data sets with the same summary statistics can look when graphed, check out Anscombe's quartet
When you are designing a research project, your choice of methods is guided by your research questions and hypotheses, combined with your knowledge of the limits of the tools that can be developed. These same research questions and hypotheses can guide the development of visualizations.
When constructing your data set:
Or, If you are working from an existing data source:
When selecting a visualization type, consider: