Facebook logs data about you and how you use their application. I know this. You know this. From there, Facebook makes inferences and serves you ads that might be relevant. Data Selfie is a Chrome extension that attempts to log similar data about you so that you can see what Facebook sees.

The data stays local on your computer, and you can export it or delete it. You also get a dashboard view of the data with what you liked, viewed, and inferences based on a combination of machine learning algorithms.

Grab the extension here.