I'm just now digging into this subject, so I can only share what I know so far.
A certain amount of techno jargon is required:
A Facebook pixel is a few lines of HTML code that is added to the <head> section of a page(s) of a website.
Whew! That wasn't so bad, right?
If a visitor to that page does a specific action, like click on a link to another page, or fill in a form (there's a list of Standard Actions at the Facebook pixel guide page) that triggers the Facebook pixel code to also take an action. If the visitor to your website has a Facebook account, then they also have a Facebook User ID (FUID). Facebook will record the FUID and tell you what they did on your website.
The next time you run a Facebook ad, you can tell Facebook to target visitors to your website (who have a FUID) who took specific actions. Facebook can also build lookalike targets - people who never visited your website (who also have a FUID) but who resemble the people who did visit in some particular ways.
Take a look at this video interview with M D Cooper:
Starting at 23:35 he starts talking about how he uses the Facebook pixel for re-targeting.
From Facebook:
https://www.facebook.com/business/learn/facebook-ads-pixelMy website is unusual since I'm using forums software as an experiment. I just use the front page as the landing page.