A cross section is a common method of depicting the internal arrangement of a 3-dimensional object in two dimensions. In many cases, though, horizontal cross sections alone, don't give enough information about the real nature of the object they depict. Vertical cross-sections can help in this cases by giving another view into the object.
Have a look at the images in the slideshow below. All the images are, in fact, horizontal cross-sections of a certain object. Looking at this horizontal cross-sections only, one would hardly get the impression about the object they have been cut from. Could you guess what it is?
Probably not! But look now at the vertical cross-section of the same object, cut, off course, in the right place:
This kind of cross section gives a much better idea about the object we're looking at. It is now much easier to decide what the object really is. Take a look!
In meteorology vertical cross-sections are used because of the exact same property: they give additional information compared to the information gained from the analysis on horizontal levels.