(Android Open Source Project)
The open-source software that is the basis for the Android smartphone OS. AOSP is a fully-functioning smartphone OS by itself, but does not include Google apps or services.
Most Android phones sold in the U.S. use the full Google version of Android, licensed from Google. Google requires that such phones include certain Google apps (like Gmail) and the Google Play Store for purchasing and downloading apps and content. This package of Google software also includes behind-the-scenes Google software that some third-party apps use. A phone that only runs AOSP does not come with any of that Google software.
Since it is open-source, any manufacturer can use AOSP, customize it as they wish, and ship it on their phone without Google apps and without needing Google's permission. This is common in many parts of the world, most notably China.