Zeiss optics refers to a set of lenses presumably made by Zeiss - a company known for making very good lenses, from sniper scopes to camera lenses. A device, labelled with "Zeiss optics", must have lenses that were made by Zeiss. Hence, to answer your question "what does it do exactly?", it basically allows the user to take photos.
Note that given the size of the lenses in mobile phones, the differences in image quality between a Zeiss-labelled camera module and one that is not "Zeiss-labelled" is rather hard to determine. So, if your question is "what can it do which other phones that are not Zeiss-labelled can't?", the answer would be close to "none".
For mobile phones, image quality is mainly determined by the aperture and the quality/build of the sensor. Lenses at that size pretty much have the same performance. However, when we begin talking about professional cameras, Zeiss lenses (especially the top of the line lenses) perform really well.