I use it and it's awesome! It's not just a video, you can copy-paste from it if you want.
Here's another one I want to try for a long time but still haven't (to have a single, animated SVG file, still copy-pastable): https://github.com/nbedos/termtosvg .
You can't add voice into asciinema itself but a asciinema recording URL would be an excellent handout material (like powerpoint) to give to students. Your students can view Terminal action with very clear text, unlike videos where reading text can be difficult.
Even if you use other method for recording/delivering your voice/audio lecture, including Asciinema replay link would be a huge benefit to students.
I'll also plug a little tool I wrote to supplement asciinema: asciiscript [1].
Basically if you get tired of watching yourself fix typos in your recordings, you can script stuff ahead of time and then record it automatically with asciinema. Although I don't think it works with programs that take input, like a REPL unfortunately.
I think it's excellent but it is limited to just the terminal. I don't think it's possible to incorporate a voiceover or soundtrack which you may sometimes want to do.
Here's another one I want to try for a long time but still haven't (to have a single, animated SVG file, still copy-pastable): https://github.com/nbedos/termtosvg .