"Variants" are typically used / related to "Page Manager", which is part of the CTools module. The "simplest explanation***" is ... not "simple" 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:
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 "page variants", 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
Blocks APIs to accomplish this.
So that's part of the changes coming up in the CTools module in D8.