Beged Kefet are six Hebrew letters that change their sound depending on their place in a word, unlike all the other Hebrew letters, that keep the same sound everywhere (If you ignore the letters that can also be silent, but that’s exactly what we’re going to do). This difference is marked by a dot in the middle of the letter, called a דגש /dagésh/.
There is just one problem, half of them don’t actually change in Modern Hebrew. In fact, in most traditions of Hebrew pronunciation at least a few of them didn’t change. Only Yemenites preserved the differentiation in all of them, which is why people sometimes think it is the most “authentic” Hebrew pronunciation tradition. I’ll try to explain why I think that is a little misguided.
Originally, these letters probably only had one pronunciation, and at a certain point the pronunciation of the letters changed after a vowel. Similar changes probably occurred in Aramaic and Greek. Now, I’m not a scholar, and I’ve yet to find a good article that actually deals with this issue, but to me that strongly hints that the change occurred during the Hellenistic period. So even assuming that Yemenites completely preserved the pronunciation of Hebrew (and that is probably wrong for other reasons), they would be preserving the Hebrew of the Second Temple period, and not before that.
Anyways, the rule is: when the letter is at the beginning of a word or after a consonant it gets a dagesh. If it is after a vowel, it loses the dagesh. The rule every kid in Israeli school ends up memorizing when learning nikkud is: בגד כפת בראש מילה /béged kéfet berósh milá/ “Beged Kefet at the beginning of a word”. I’m not sure why, it doesn’t help much, and it’s only half of the rule, but anyways…
Here are the different pronunciations of the בגד כפת letters:
Bet and Vet: בּ – b, ב – v
Kaf and Khaf: כּ – k, כ – kh
Pei and Fei: פּ – p, פ – f
Gimel, Daled, and Taf stay the same everywhere, but if you want to right correctly with nikkud, you have to put the dagesh in them in the right places.
Obscure point to impress your Israeli friends with: in a few ancient sources ר is also included in this group, with the difference probably being aspiration, like in Greek. Most people have never heard of this as the main source for it is an ancient Kabbalistic text called ספר יצירה /séfer yetzirá/ “book of creation”.