In order to successfully describe your website to the search engines, you need to use a vocabulary that the search engines will understand - that is, Structured Data.
Structured data is data that conforms to a predefined data model that describes your website content in such a way that makes it far easier for the search engines to understand, which means your likely to benefit from this in your SEO efforts.
The vocabulary that's used by the main search engines 'Schema.org', which basically translates your website content into codes that the search engines can process easily. After processing this code, the search engines can present their search results more intuitively.
As each minute goes by, the Internet grows in size and complexity. Imagine the colossal task the search engines have in trying to regularly index the whole Internet. Then factor in that every time a search engine visits a page, there is an actual financial cost to this (electricity, bandwidth, servers etc), so the search engines are always looking at the most efficient way to index sites to keep costs at a minimum. Finally, factor in 'time' and try to imagine how long it would take you to index over 55 billion pages, then go back and do it all again. Mind blown.
Considering the above, it makes perfect sense that the search engines like 'structured data' as it increases the efficiency of their indexing process. Efficiency aside, structured data also presents information about your site in such a way that the search engines can better understand your content, which means they'll be able to rank your content better in the SERPs.
Structured data gives you the ability to control how your website structure is defined, which therefore gives you control of how search engines understand your website content.
As mentioned above, with more than 55 billion pages on the Internet, there's a huge amount of duplicate and low quality content that the search engines wants to keep out of their indexes. So, by having structured data, this helps the search engines find your content easier, understand it better and it's therefore (assuming its valuable content) quicker and easier for them to include it in the relevant SERPs.
With structured data, there's a good chance you will get some 'rich' results appear in the SERPs, which is a great way to increase CTR as your rich media snippet will stand out on the SERPs and encourage users to click on your link.