What people did they find there that made their conquest of the peninsula unfinished? How did this people manage to keep them off their land? Were there other reasons for this sudden stop in the conquest?
Yes, well there are a couple of big reasons that add up: First the caliphate conquered the visigoth kingdom pretty easily and strive onwards to the merovingian kingdom(aka the franks), they got momentum, troops, and a fairly good timing due to the incompetence of the merovingian king to rally his lords behind. Why they did this and not finishing conquering the iberian peninsula first? Well frankia was much more rich, in resources, in farmlands, in trade power over the mediterranean due to the south of france being a center of commerce still (not what had been during the roman times but still Henry Pirenne-Mohammed and Charlemagne), they were the only and last big european power, and they weren't in any good shape, rebelious lords, poor economy, not unify, etc. So the arabs took their chance, it wasn't a conquering party though, it was a scouting/rading, they were far off arabia, streched a lot their supply lines and their manpower, they didn't see a point in going so far from their homeland for such little (just like the huns or mongols did; I mean in general the best defence of western Europe against external invaders always been that's its shitty, really geographically fragmented, really cold, really poor farming lands in general, and not many resources at least obtainable at the time). When they lost against charles martel, they stopped the arab momentum, they had enough land, the caliphate was breaking up, so internal turmoil, and then the spanish calipahte got separated from the rest, and start internal fights for the succession, so they were more interested in fighting between them and administrating the land, probably if one would have tried to conquer Asturias his taifas neighboor would try to take his kingdom. The only bit that survived from christian spain was Asturias (aka "north of the iberian peninsula"), and once they conquered almost all they sent a small rading party(~800 men) and were driven off by king Pelayo(~300) in the Battle of Covadonga. Asturias was poor, only resource was fish, it was rocky and mountainous, didn't have commerce or a good port, not anything of value for the muslims, and the people there knew very well the area, and guerrilla tactics, and were determined to fight till death, they present no match whatsover for a caliphate that can muster 30thousands against at most 1000 of the asturian kingdom. So they didn't even care for a bloody and useless campaign with high death toll for so little.
TLDR: Asturias was poor, and ugly to made it a n interesting conquer for the muslims.