KoBoToolbox is based on elements from several other open source tools, most importantly pyxform, formhub/onadata, and the OpenDataKit. As a result, all forms and collected data are compatible with these tools.
The best way to use KoBoToolbox is on one of the two public instances - kobo.humanitarianresponse.info (if you work for a humanitarian organization) and kf.kobotoolbox.org (non-humanitarians). There is no software to be installed on your computer. Installing KoBoToolbox on your own computer is not necessary and is only recommended if you work in an environment with absolutely no Internet access.