Symfony is a set of reusable PHP components, which can be used seperately or as part of the Symfony Framework.
As most frameworks, Symfony solves recurring technical problems for you (such as authentication, routing, etc.) so you can focus your time on the actual business problems you’re trying to solve.
In contrary to other frameworks, however, the Symfony components are decoupled from each other, allowing you to select the ones you need. Instead of having to adapt your application to your framework, you can adapt the framework to your needs.
This is what makes Symfony very popular and allows other projects and frameworks (including Laravel, Drupal, Magento and Composer) to utilize the components without having to use the full framework.
Symfony is an open-source project. See how you can contribute.
The official Symfony documentation can be found on the Symfony website.