Structured data is data with a high level of organization that helps Google list your website more professionally. This organized data could be things such as an event or reveiew ratings.
An understanding of these organized types of data helps Google understand your website better. With a better understanding, your search rankings improve and your website is portrayed more professionally.
Working with structured data requires use of the webmaster markup, but Google has made it a bit more simple through its data highlighter tool.
Take a look at this video explaining the use of data highlighter.