Fire OS is a Linux kernel-based mobile operating system produced by Amazon for its Fire Phone and Kindle Fire range of tablets, and other content delivery devices like the Fire TV. It is forked from Android. Fire OS primarily centers on content consumption, with a customized user interface and heavy ties to content available from Amazon's own storefronts and services.
While the Kindle Fire line has always used customized distributions of Android, particularly 2.3.3, API level 10 (Kindle Fire) and 4.0.3, API level 15 (Kindle Fire HD), Amazon only began referring to the distribution as Fire OS beginning with its third iteration of Kindle Fire tablets, which includes the Fire HD 2nd generation and Fire HDX models. Unlike previous Kindle Fire models, whose operating system is listed as being "based on" Android, the Fire HDX "Fire OS 3.0" operating system is listed as being "compatible with" Android; Fire OS 3 is forked from Android 4.2.2. In the Fire HD (3rd generation) and Fire HDX (2nd generation) tablets, Fire OS 4 is included that is forked from Android 4.4.2 (API level 19). Since then Fire OS 4.5.1 update has been released, and Amazon's OS said to be based on Android 4.4.3
Source: Wikipedia, "Fire OS", available under the CC-BY-SA License.