The FOSS movement, free open-source software, is all about programming freedom. With FOSS, anybody is free to modify, change around, and fork the code as they please, with no proprietary code whatsoever to slow them down or make implementation or modification harder than it needs to be. While Android is open-source, meaning that the underlying code is free to be messed about with under certain free license conditions, Android is certainly not FOSS. Nougat and the Jack compiler doing away with Sun and Oracle's Java is a step in the right direction, but the OS still has proprietary bits from Google under its skin. The Replicant project has long sought to change that, and has brought Android to FOSS enthusiasts for some time.
The project is currently on Android 4.2 Jelly Bean officially, but work on Android 6.0 Marshmallow is underway, and has almost reached daily driver status on the initial guinea pig, the Exynos variant of the Samsung Galaxy S3. The main developer of Replicant, Wolfgang Wiedmeyer, is personally working on stabilizing some of the features to get things to a fully FOSS status and up to a daily driver level of stability for Marshmallow. Currently, the focus is on graphics acceleration and creating toolchains from scratch. Development takes place in the forum, with the developers and users talking over changes together before they're put into the official build and shipped out.
Replicant is not only unique from stock Android in its rejection of any non-free software in the OS itself, but it gives users a special marketplace, called F-Droid, that allows them to seek out FOSS apps and resources. While a huge number of apps out there are not FOSS compliant, users looking to go strictly FOSS for ideological purposes should be able to perform most of the basic functions of a smartphone with the OS, even without Google's services. The F-Droid marketplace is currently having some issues with Marshmallow, making the test build for the Exynos Galaxy S3 a bit unstable. Once upstream Linux code gets more deeply integrated, however, the project will be much easier going forward. For now, if you're a FOSS enthusiast who wants to see if Replicant is available on your device and possibly contribute, head through the source link.