Replicant is an open source OS for Android phones, while Android is built on a Linux kernel and claims to be open source, in reality it contains proprietary libraries and drivers necessary for interfacing with the phone’s hardware, these include the GSM radio interface library, bluetooth firmware, speech recognition and others, Google has allowed vendors to introduce their own closed source binary drivers into the system that the community can not redistribute, it also uses pushes its own proprietary apps into the system, like Google Maps, Gmail and Gtalk.
The Replicant operating system intends to replace proprietary drivers and have Android run 100% free software.
Because Google Market is proprietary software, Replicant uses a client app released under the GPL license called FDroid that comes with its own repository full of free and open source software (FOSS) apps, it doesn’t include any Google app and comes with alternatives that do exactly the same, you can use Google Market apps in Replicant phones without using Fdroid, but this is not encouraged. Fdroid can also be build in Linaro, a set of tool to help popular Linux distributions run on ARM computers.
Installing Replicant on your phone will void the warranty, eliminate Android OS and erase the data it holds, but if you are a hardcore open source supporter and can risk something going wrong it is probably worth it, check the list of supported devices on their website.