The descriptions entered in the (custom) user profile fields is not displayed anywhere in Moodle. If you add a new user, you can see the profile field, but you cannot see a description which would be useful for explaining how to fill out the field – especially if it is a link to something that requires a specific format.

Note: These descriptions only need to be visible when the user is EDITING the profile. They don't need to appear when just browsing the Moodle site and viewing a profile.

This is also a User Experience (UX) issue. The best possible way to solve this issue came from michael-milette in the MDL-56367 issue related to this topic. I will quote that comment here:

Instead of making it optional to display the field description, what if the contents of the description field could me made to optionally appear in a Help bubble, similar to other built-in fields? I think that would be very useful. The default would be to not display it for backwards compatibility.

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Site administration - Users Accounts - User profile fields

The description is not rendered. (tested with Boost, Classic and commercial themes)