The short answer: SDH subtitling is closed captioning for DVD.
The long(er) answer: because closed captioning has been traditionally restrictve in terms of, for example, colors, fonts, and line length, the DVD industry decided to create a special form of subtitling that would uphold the spirit of closed captioning while maintaining a greater degree of stylistic and format flexibility. Subtitles for the Deaf and Hard of Hearing (SDH) will have the same style and formatting options that mainstream foreign language subtitles will have, but they will maintain the speaker indentification and sound effects you would find in a closed captioning file.
Film festivals, cinemas, and DVDs are perfect locations for SDH subtitles. Each of these entities embraces the most flexible subtitling formats, and SDH subtitles will provide your entire audience with the option of "reading" the audio regardless of how well they can hear it. (Note: Because SDH subtitles are associated with the U.S. DVD industry, they are normally English files.)
There are dozens are various file formats that would work for SDH files. Here are a few of the formats you might expect to see with SDH subtitles: