Joomla! 3 is packaged with Bootstrap 2.3.2, which is the latest Bootstrap 2 version ever released.
Simplify Your Web extensions, ever since the beginnings of Joomla 3, have been using the version of Bootstrap included with the Joomla core.
Although all versions of Joomla 3, for the sake of compatibility, remain on Bootstrap 2, more and more templates have evolved and moved on to use Bootstrap 3 or the latest Bootstrap 4.
All is fine if templates are Bootstrap 2 compatible. The extensions' output calls Bootstrap 2 and is showing Bootstrap 2 elements correctly (labels and pagination arrows are properly skinned, for instance).
Things go sour when the template is made for another version of Bootstrap. Elements are not necessarily skinned the way they should and worse, different versions of Bootstrap may end up loaded at the same time, causing conflicts.
The Bootstrap compatibility parameter, now part of the Simplify Your Web extensions needing Bootstrap for specific components creation, is trying to address issues you may be having with Bootstrap.
Select version 2, 3 or 4 to ensure that the code generated by the extension is compatible with the Bootstrap version your template is using (you may need to find this information out from the template's documentation).
In these cases, no Bootstrap version is loaded by the extension, it just uses the Bootstrap version the template is already loading.
If your template is not based on Bootstrap, select the joomla option, which is meant to load Bootstrap 2.3.2, packaged with Joomla, only when necessary. The Simplify Your Web extensions use code that is standard Joomla 3 code, ensuring that no multiple versions of Bootstrap are loaded on your page at one time.
