Typically zero does exactly what it says – sets the micrometer’s reference zero to whatever position it is at – so close up the micrometer until it is closed, with the same force/technique you would use on a workpiece, and press zero. It is now set.
abs/zero usually switches between displaying the ‘absolute difference’ between where the micrometer is and the set zero point, and displaying a ‘relative distance’ from a temporary zero when you press the button. This saves you resetting the main zero point if what you want to measure is the difference between two sizes.
This latter is very useful if you are turning a shaft to a size – set the micrometer to read the size you want, switch to relative zero mode, and it will read the difference between the size of your bar and the target size. When it reads zero, switch back to absolute mode to check it has worked.
There are quirky differences between different types so practice a bit until you are 100% confident it does what you expect.
Neil