What do these div' classes mentioned below do?

Classes and IDs can be assigned to HTML elements like divs to allow them to be targeted with CSS for styling, and also by other front-end languages like JavaScript, and JavaScript libraries like JQuery.

If we were to write an HTML page with no associated CSS (or JS), any classes and/or IDs we assigned would do nothing. However, HTML is rarely written to work in isolation. The Wordpress core, themes, and plugins all generate HTML pages which will typically have some CSS to go with them. The developers will probably have created style rules in the CSS that goes with their HTML (which is actually generated by PHP in the case of Wordpress) which changes the way the page content appears in the browser. They may also have created sensible classes and IDs for elements, but not styled them, in order that other developers may come along and style their content.

So the classes you refer to are generated by Wordpress, most likely by the theme.

<div class="wrapper"></div>

This class is most likely assigned to the div element which contains the page content or a large section of content.

<div class="profile-image"></div>

This class probably wraps the img element for a user's avatar image, and so on.

If you learn how to use CSS with Wordpress, you can assign style rules to these elements and classes to change the way those elements are displayed on the page. You could also learn how to use the different browsers' developer tools to inspect the HTML and CSS of any page you view. I'm sure several Treehouse courses cover how to do these things in great detail!