A vanilla, plain version of Android is one which uses the Android interface and apps as supplied by the Android Open Source Project (AOSP) and doesn't modify those in any way. A Vanilla Android OS may often include custom (and proprietary) drivers required to take full advantage of a device's hardware, and may also include a few extra apps to take advantage of that device's hardware or access a phone network's features, but will be otherwise unmodified.
All "Pure Google Experience" devices, such as the Google Nexus range of phones, are supplied with an unmodified, plain, vanilla version of Android as standard. Additionally many budget devices from smaller manufacturers run vanilla Android with little to no customization.
Some custom ROMs pride themselves on being a vanilla, AOSP version of Android that their users prefer to the customized versions installed by default on the phones.