google creates the "vanilla android" software. by vanilla I mean base, plain jane code developed around ASOP (android open source project). Cellphone manufactures then take the vanilla android code and add in different elements to the user interface (UI) to make the operating system their own. Motorola uses "blur" as their name for their UI "improvements" they make to android. HTC uses "Sense", samsung uses "touchwiz". each is a little different and each has differnent features, but all are based from vanilla android.
You will see custom ROMs form many developers that say "blurless" meaning they have removed the added items (widgets, apps, settings, options, themes) from the Manufactures software and the UI is basically vanilla android.
Think of yourself as "android" and the clothes you put on and wear as "blur" you are still yourself but you look/act different from other people (Sense, touchwiz), but your still all human (android)