Object Summary
WP_Post is used to access all data that makes up a post. It's not difficult to implement since it gets all its data from the database, and then all of accessible fields are named with what they store. It's also simple from a class perspective; there are just the general class methods. In addition, it can filter content. I'm not sure what the difference between getting the class and getting an instance of the class is because that feels like the same thing, but there's that.
Object Data
It stores both what you edit directly as well as other information about the post. For example, post_title and post_content get the two most-used parts of a post. Others like post_date and comment_count happen as a result of actions on the post, whether creation or commenting. Post_date and post_modified have an alternate version that get data using GMT. Finally, you can access information through foreign keys like post_parent getting the ID of the parent post.
Object Role
Any functions that retrieve data about a post are supported by WP_Post. You don't actually have to interact with the object directly as PHP takes care of that in the functions, but said functions still represent the fields available in the class. A large purpose of WordPress sites is to display posts, which can be gotten through a loop to display as many as you'd like. WP_Post is used for such displays.
Summary
I would argue that WP_Post is the most important WP class. Without it, you couldn't interact with your most important site content. WordPress makes this process even easier on you since you don't need to interact with the class directly, but anything you need about a post is still accessible.