What causes a random giant mouse cursor?
El Capitan introduces a feature for finding a mouse cursor you've lost. Shake the mouse around and the cursor will increase in size whilst you're shaking so you can find it.

Here's the moment it was introduced in the Apple Keynote at WWDC 2015:



You can disable this feature in System Preferences → Accessibility → Display.


  Shake mouse pointer to locate
  Quickly move the mouse pointer back and forth to make it bigger.