Vector based map servers generate much smaller XML files for regions of the map that contain information about lines, text and areas. It is the device that caches renders these using hardware acceleration. The server can generate and cache these XML (PBF=protobuf file) files much faster and since they are generally 1/10 the size of the PNG files and GZIP compressed so the data transfer and device side caching is correspondingly faster and more efficient. Since the rendering occurs efficiently on the device, pan and zoom is much smoother. We also have the advantage of dynamically applying styles to the map when it is rendered, allowing KayakNav to support various day and night modes. In addition, vector tiles make it much simpler to rotate the map and have the labels automatically re-orientate themselves. Check out the following link for a detailed video of vector tile features.
You can test this vector tile server by clicking one of the following which are now served via HTTPS to suit iOS9 requirements: Lake Ginninderra, Sydney, Paris, London, New York, Queenstown NZ. You can download a single vector tile but will not be able to make much sense of the binary content in the PBF file.
Check out how MapBox host their maps.