Primal Ancient Legendary items in Diablo 3 is a type of Legendary item that is even better than the Ancient Legendary items. If you want to get Primal Legendary you need to beat a Great Rift Rank 70 solo on any character on that ladder. This means that you will only unlock it for the characters in the same season and league (hardcore or softcore) as the character you beat GR70 on.
Once you beat a Greater Rift rank 70 you will unlock the chance for any Legendary item to drop as a Primal Ancient Legendary instead, with a very low drop chance. Any character in the same league and season can get the drops even if that character has not beaten GR70 themselves.
Primal Legendary items are the strongest Legendary items in the game, so you should definitely pick them up and see if they are useful to you. Set items can also drop as Primal Legendary items, following the same requirement (GR70 solo) as for regular Legendary items.
A Primal Legendary item will be indicated by a red beam on the map, instead of the regular orange beam for Legendary items. This is also reflected on-ground where it shows a big, red beam.
Like with all items, the drop chance is higher when you play on a higher difficulty, or do a higher Rift rank. So don't expect to find many of these if you play on low torments, even if you have completed the requirement to unlock them.