Quick search of the forum brings up:
Precursors, as the blurb states, are robot ships that guard some of the ruins in the game and small Precursor ship occasionally appear in non-ruin system. Leave this selected as Precursors provide valuable combat experience. Rather than a complete Empire similar to your own (which is what NPRs will be). Precursors are isolated groups of ships left over from an ancient Empire that dominated the galaxy until they were destroyed by a foe that is yet to be introduced to the game. All that remains are the few ships that guard the ruins of defeated foes waiting for new instructions that never arrive. Their mission is simply to eliminate all non-Precursor life. They have no real populations, although they may have small listening posts and weapon caches in the system. Although few in number and they don't have any survey ships for exploration, they are likely to be higher tech than your own Empire at game start and any starting NPRs. You will need to overwhelm, outsmart or simply avoid them until you are ready.
Leave the number of computer-controlled Empires (NPRs) as 1 and leave the two checkboxes in the section checked. One NPR is plenty for a starting game as new ones will be generated as the game progresses and new systems are found. An NPR is an Empire much like your own. It will be exploring the galaxy, encountering and fighting Precursors, setting up new colonies and improving its industry. When you finally encounter an NPR it may turn out to be friendly, depending on how diplomacy progresses, or it may be an implacable foe. Or it may change from one to the other at some point.
There is another relatively recent post that should have more info on what Steve 'thinks' they are when he runs into them during his fictional campaigns but I don't have the time to search for it too.
Pretty much just do a search for Steve's posts with some key words and you will find the official explanation for things.
