MKV does not play on iPhones, in QuickTime or in most browsers and editors. ASS gives full control over how subtitles look. MKV is at home in films with several audio and subtitle tracks; ASS is the usual choice for anime and karaoke subtitles with fonts, colours and positioning.
One MKV can produce several ASS files; when it does, they are offered together as a ZIP download. This is demanding work for a browser: a long or high-resolution file can take several minutes, and your device does all of it, so keep the tab open.
This pair uses the compatibility engine, ffmpeg built for the browser, because ASS cannot be written by the browser's built-in codecs. It is a one-off download of about 10 MB that the browser keeps, it is slower than the built-in codecs, and it takes files up to 1 GB. Only text subtitle tracks stored inside the video are extracted, one ASS file per track (several tracks come as a ZIP); picture-based tracks from DVDs and Blu-rays are refused because they would need text recognition. A feature-length file is fine, since the video is only read and the result is a few kilobytes.