Component APIs are an advanced feature. An understanding of how Unity works is required to utilize them.
A Component is a collection of functions and variables that allow you to control object behavior.
Components are a Unity concept, they're the building blocks that Tabletop Simulator objects are composed of.
Every object in Tabletop Simulator is a GameObject. When a game is created, GameObjects are loaded, initialized and some of these top-level GameObjects are then exposed via Tabletop Simulator's Lua scripting APIs as regular Objects, each with their own scripting contexts.
Some Lua-exposed Objects are made-up of hierarchy of children GameObjects. The Component APIs allow to access and interact with these children GameObjects (which you'd otherwise be unable to control).
GameObjects are themselves made up of Components. A typical GameObject would contain a Collider, Transform, Mesh etc. These Components describe the GameObject's behavior and visual representation.
In addition to built-in Objects, the Component APIs provide access the GameObjects and Components that exist in AssetBundles. This means that when creating an AssetBundle, you may attach all manner of components (lights, sounds etc.) and you'll be able to control them via these APIs.
Each Component has Vars. These are variables which you can modify to change how that Component affects the GameObject it composes.