It may seem strange to write about text-based browsers, when graphical ones are the norm. But it isn't—it's even necessary and here I'll explain in detail why.
Braille readers, used by people with disabilities, can read only text. If the text is unavailable or logically incorrect, the user won't understand the intended message. Braille readers can't transform an image or video into speech without an alternative textual content, provided by the designer.
Search engines prefer textual information over images, when indexing a web page. Search spiders can't index multimedia in a textual form, unless it has an alternative textual description. The lack of such information hinders the spider's understanding of the content. A descriptive "alt" attribute in an "img" tag fixes this issue. It's even mandatory if your page must validate.
Lynx is one of the most popular text-based browsers. After starting it, you may browse normal websites, typing "g" and then the address. Lynx shows you then how the website is normally seen by search engine spiders. This allows you to test if your content in you fallback version is accessible when nothing else works. You can also use it to think about better titles, headings and keywords to describe the purpose of the content. Take a look at the Lynx 8 for more information.
Viewing a web page in a text-based browser allows you to concentrate only on the text, discarding all images, media and scripts. Users may disable images in their browsers to access the content quicker or disable scripts to avoid security threats. In all cases you should provide a concise and representative alternative. While testing the textual content is possible on a full-featured graphical browser, it's also more distracting to do it there.