What is .?
A pause in Lojban. Otherwise a period, or a little funny dot. When are pauses mandatory
As The Book says in Chapter 3, when a pause is required, the minimal pause is a glottal stop. You are, of course, allowed to pause longer if you wish.
Many other languages, including English, use glottal stops. If you are an English speaker, say the word "if" in isolation (or any other word that starts with a vowel). The tiny catch in your throat before the vowel is a glottal stop.
Next question: why is .? Why that symbol? It is often written as ', but ' was taken.
And another: doesn't a little . magically/naturally appear, for instance, when you cut into or out of a recording while a vowel is being played?
Yes.
--So how does one deal with that in lojban?
Um, no problem. It just works. Remember, . doesn't mean "glottal stop," it means "pause," and glottal stop is an allophone of pause. When you cut into or out of a recording, there is silence from the recording before the incut or after the outcut--that's what cutting in/out means. Therefore, there is quite correctly a pause/glottal-stop/Lojban-dot in that place, and if we were transcribing the sounds, a period would be completely appropriate to write there. Note also, that the period is never mandatory to write (though the pause may be mandatory to say), so long as you have at least spaces in the right places.