Why might you want to close-caption or subtitle video content on your site? Well, one reason for subtitling is to provide fully functional internationalization/localization capabilities. One of the many reasons Drupal is the CMS of choice is because of its robust multilingual support. If you are posting multilingual text content on your site, multilingual support can and should extend to all content, including video, through the use of subtitles.
Many visitors to your site—regardless of whether or not your content is internationalized—may use a screen reader or require the use of text captions where audio is used within video to convey information. It is therefore a reasonable accessibility accommodation in many cases to provide closed captions where video is an essential component of your site.
A third use case involves a site where video is used to demonstrate a process in detail, but where audio description is too expensive, time consuming, or creates significant localization challenges. I have a site where I have hundreds of separate videos, all with stepwise descriptions for completing maintenance or troubleshooting procedures. I needed the non-technical end-user to be able to upload the video and add subtitle text in the node edit page.