These are JPEG compression artifacts, caused by Facebook when it processes and often rescales uploaded images, and adds more lossy compression. If you follow Facebook's help guidelines for making sure your images are displayed at the best quality, you should be able to ameliorate the problem.
Here's what they say:
We automatically resize and format your photos when you upload them to
Facebook. To help make sure your photos appear in the highest possible
quality, try these tips:
Resize your photo to one of the following supported sizes:
Regular photos: 720px, 960px or 2048px wide
Cover photos: 851px by 315px
To avoid compression when you upload your cover photo, make sure the file size is less than 100KB
Save your image as a JPEG with an sRGB color profile
You can also changes your settings so that your photos are uploaded in
HD by default.