As pointed out, anime subtitles are either .ssa or .ass, which not a lot of devices support. Apple devices definitely don't, but they do support .srt subtitles.
So there are two options: re-encode and hard-sub it with Handbrake. This should work for the most part, but it's time-consuming, and Handbrake is still imperfect with complicated subtitle styles.
What I do: extract the .ass with MKVTools, re-save as .srt with Jubler, and remux into an mp4 with Subler. You will lose the formatting, styles, fonts, and karaoke effects. I don't mind watching subs that way since it's much easier than hard-subbing and I still get subtitles, but if retaining those are important to you, for most devices, the only option is to hardsub it.