AOSP, stands for “Android Open Source Project,” is an open-source software project that provides a base for the Android operating system’s development. The AOSP is basically just the code without any Google services, apps, or APIs included in it and can be used to build modified versions of Android
The problem with this though is that if you rely on Google Play Services then your app won’t work as expected because these are not compatible with different devices.
This is where the AOSP+GMS comes in. This combines Google Play Services with an Android OS that has no API level 15 and higher preinstalled (API Level 16 was released in October 2015).
The advantage of using this version over just using AOSP is because it includes apps such as Gmail, YouTube, Hangouts, Drive etc.