"Let’s talk about Action Bases”
Okay!
"What exactly are they?”
It’s just the name brand for Bandai’s official model kit stands.
"I guess that means that the models don't come with their own”
That depends on the model. The general rule is “if it can’t stand, then it comes with a stand.” Any spaceship or Mobile Armor should come with one. For example, all of the spacecraft from Bandai’s line of Star Wars kits do.
Additionally, there are times when humanoid models come with a stand. For example, all of the Gundam G Frame figurines come with one, and most (if not all) of the humanoid Star Wars models come with stand to help them remain standing (even if they are kind of dinky).
In other cases, a given product line will have the occasional one-off model that comes with an included stand. This may be because the model is super expensive/super premium, or maybe it is small enough (or simple enough) that they needed to throw a stand in there to justify keeping it the same price as other products in the line. For example, most Master Grade Gunpla do not come with a stand, but the Wing Proto Zero - a model that is so small and simplistic that it’s considered one of the easiest MG’s to build - does.