What is a "Variant" in Drupal?
&quot;Variants&quot; are typically used / related to &quot;Page Manager&quot;, which is part of the CTools module. The &quot;simplest explanation***&quot; is ... not &quot;simple&quot; to provide. However there is an interesting (amazing?) video intro about it: refer to Learn Page manager! Part 3: Variants and selection rules.
While you're at it, you may want to look at the entire (impressive) video series around there, i.e. Learn Page manager!. Here is a summary of the entire set of videos about this topic:


Page manager allows you to collect and manage contextual information in a flexible and consistent way. It is an important part of building infrastructure on Drupal websites, and you should know how to use this module.
The screencast series is targeted at experienced Drupal developers.
Episodes 1, 2 and 3 introduces the most basic concepts, such as custom pages, variants, selection rules and (to some extent) contextual objects.
Episodes 4, 5, 6 and 7 talk about Panels, with emphasis on Views integration but also some words on efficient caching.
Episodes 8 and 9 about access control, menu items, and not least the little-known but very useful Contextual Administration module.
Episodes 10 and 11 talks more about using contextual objects in Page manager, including using Views as context. This is, imho, where the real power in Page manager is.
Episodes 12 and 13 collects various bits and pieces, such as how to use Panels to easily rearrange the node edit form, import/export settings, and some extra modules that can be used with Page manager.


Some more recommended (free) tutorials that you may want to consider, and which will help a lot to understand the typical Drupal terminology in your question:

The 32 (!!!) great video tutorials Learn the Rules framework, organized in 7 chapters, about the Rules module.
A similar set of 8 video tutorials about the Flag module.
The set of 30 video tutorials about the Views module.

In Drupal 8, Page Manager has become a separated module, while formerly (up to Drupal 7), it was part of the CTools module. Here are some more quotes from the (D8 related) project page:

It supports the creation of new pages, and allows placing blocks within that page.
Like Drupal 7's Page Manager, it provides a concept of &quot;page variants&quot;, each with their own selection conditions.
Additionally, it can be used to take over an existing page, like overriding /node/% to change what is displayed when viewing a node.
It utilizes the core Conditions, Context, and Blocks APIs to accomplish this.

So that's part of the changes coming up in the CTools module in D8.