The content search web part is a new web part introduced in SharePoint 2013. It show you dynamic content based on a search query. The query and the results can be customized trough the web part properties and by using display 
templates.
When you want to learn more about the Content Search Web Part you can start here:
- Content Search Web Part in SharePoint 2013 (MSDN)
- The Content Search Web Part to Display SharePoint Subsites: nicely explained by the guys from ShareGate.
When you start exploring this you can discover the following issue I encountered:
I was able to add the CSWP to a custom page and was able to modify the parameters. The test results were visible but when confirm the details nothing was visible on my page. The solution was to enable the cross site publishing feature on the site collection. Be aware of this! 😉
Exploring the Content Search Web Part http://t.co/NQxgtggH7i #SPums