The Serif and Sans-serif sections contain fonts that should be suitable for body copy, smaller sizes, and longer passages for sustained reading, as well as user interface work (and of course for display or headings, large sizes). The Display fonts are intended for headings and the like, and generally have fewer styles available or are missing italics, etc. The Display faces may need to be paired with a suitable serif or sans-serif font to develop an entire system, depending on the use case.
All fonts are available under the SIL OFL license. This license allows anyone to use the fonts for free in commercial applications such as print, websites and desktop and mobile applications, and to modify or redistribute fonts (under a different name, and under the same license) as long as the fonts themselves (or derivatives) are not for sale. The fonts are generally hosted by Google at Google Fonts, and generally available for download on Github. (Sometimes the Github repos feature better OTF downloads that support Open Type features not available in the Google Fonts TTF versions. Sometimes the Google Fonts versions lack features like real small caps, whereas the Github download may support this feature.)
Much ado has been made about the quality of “free fonts” or Google Fonts as a whole, and much of it is well-placed criticism. Generally, you get what you pay for, and free (public domain, gratis not libre) fonts are generally very poor in quality and a waste of time, and in my not-so-humble opinion, Google Fonts or Font Squirrel would be better resources if they had a higher standard for quality and focused on curation instead of sheer quantity. However, when a brilliant type designer such as Matthew Butterick blasts all of the typefaces on Google Fonts as not being opens source, or if anyone out there claims that the existence of lists of Top Forty Best Fonts on Google Fonts is proof that Google Fonts is a completely lost cause, that strikes me as patently erroneous.
Additionally, despite Mr. Butterick’s claims about the lack of collaboration on existing OFL or Google Fonts typefaces, there actually have been some interesting and important posthumous developments by the community on some beautiful type designs started by, for example, the late Vernon Adams, an impossibility in a proprietary-font world. This feels like a lemons-into-lemonade situation, and very much in the spirit of open source culture.
Consider the fact that the entire world of proprietary fonts is so vast, and filled with such a variety of fonts of varying quality that even the very foundational, expensive, and proprietary Adobe Font Folio includes a few strange fonts with very narrow use cases, such as dingbats of various sorts, or Critter, Cutout or Rad Std. If AFF deserves a worst-of list and a best-of list, then what does that tell us?
The fact that Mr. Butterick himself graciously guides his reader toward some wonderful (proprietary) font recommendations tells us that font selection and discovery is a hard problem, no matter where you look. If proprietary fonts are magically so great, then why do we need Best of the Year lists and Typewolf and Fonts in Use and all of that? Yes, well-designed proprietary font families are worth their weight(s) in gold, and there may be more proprietary workhorse families, but that does not mean there are not some very high quality open-licensed fonts that fit the same bill.
In addition you might elect to support type designers by paying someone to develop an existing OFL font family to your specifications, similar to the proprietary type world where custom fonts can be commissioned, except the work released would go back out into the world to everyone’s benefit. Where do you think a lot of these families came from?
See Updike.org for more about Jared Updike, and his various projects.