"The Facebook pixel is an analytics tool that allows you to measure the effectiveness of your advertising by understanding the actions people take on your website." Once you've set up the Facebook pixel, the pixel will fire when someone takes an action on your website. Examples of actions include adding an item to their shopping cart or making a purchase. The pixel receives these actions, or events, which you can view on your Facebook pixel page in Events Manager. From there, you'll be able to see the actions that your customers take. You'll also have options to reach those customers again through future Facebook ads."
The Conversions API allows advertisers to send web events from their servers directly to Facebook. Server events are linked to a pixel and are processed like browser pixel events. This means that server events are used in measurement, reporting, and optimization in the same way as browser pixel events. Learn more on Facebook Help Site.
From Facebook Developer DocumentationAs an enhancement to our existing advanced matching, we've released an automatic version of advanced matching for the Facebook pixel. This version is designed to help advertisers easily leverage their customer data to track more conversions and build larger remarketing audiences.