This is directly from the Yoast website:
The alt and title attributes of an image are commonly referred to as alt tag or alt text and title tag even though they’re not technically tags. The alt text describes what’s on the image and the function of the image on the page. So if you have an image that’s used as a button to buy product X, the alt text would say: “button to buy product X”.
If these tags are filled out, they will always write out in the HTML. Although they will not display directly to the screen. title will provide users with additional information about the image if they hover over it. alt will provide screen readers a description of the images. More on that later.
For the descriptions, this is more commonly seen on the “attachment page” for an image. But would be largely dependent on the theme developer. From Title, Caption, Alt Text, and Description: Harnessing the Power of WordPress Image Metadata:
If you add text to the description field that text will be stored as post content for the attachment post. That means if someone lands on the attachment post page for the image they will see the long description (provided the current theme supports it).
Example: <img src="https://wordpress.stackexchange.com/questions/226292/path/to/file.jpg" title="Your Title" alt="Alternate Text" />
Accessible Images
In terms of accessibility of images. If the image contains text, provides information not also explained on the page or is complex in nature an alt tag should always be used to describe the image.
If the image provides no additional value other than to break up content or provide something decorative (such as using an image as an line break) you should always use alt="".
Additional information on Accessibility of images can be found on the w3.org’s WAI Images Concepts page.