The Animations list appears in the Hierarchy when you are in Animate mode. This is a list of all the animations in your current file. By default you'll have one animation named Untitled. Click the plus icon to create a new animation. Double click on the text of any row to rename it.
In Animate mode there is always at least one animation selected; that is the animation that is active in the timeline. To make an animation active, select any of the rows in the Animations list. You can also preview any of the animations in this list by clicking the play button (regardless of whether the animation is currently selected). This allows you to play multiple animations at the same time, which can be helpful to ensure that your animations will blend properly in your game engine.
For example, you might create a walk animation for a character in your game. You might also create an attack animation. In your game, these animations may need to happen at the same time. Use the play buttons next to each animation to preview what your character will look while walking and attacking. The same attack animation might also need to work with an idle, run, or jump animation. Being able to play back multiple animations allows you to make sure that your attack animation works properly with all of these and that you don't have any conflicting keyframes that cause unexpected results.
For more details on how to work with animations, check out the Timeline page.