Although of course in medieval Christianity (as in modern Christianity) God the Father was the judge and God the Son was the savior, in day to day religious practice the saints got a lot more attention.
Originally there was no procedure for becoming a saint. If one had lived a holy life, being recognized as a "living saint," and then worked miracles after death, one was a saint. These are indeed the criteria still used, but before the twelfth century these determinations were made locally, whereas since the twelfth century they have been centralized in Rome.
Western Europe was Christianized slowly, as indeed was the whole Roman Empire, but by the fifth century all provincial capitals in the Empire had bishops. However, the west had very few saints. The city of Rome had by far the most, for its catacombs were full of bones, many of which were identified as Christians put to death under pagan emperors like Nero and Aurelian. (Early Christians had indeed met for religious service in the catacombs.)
Europe's shortage of saints was solved by the sixth century, for not only were there a number of fifth-century holy bishops who could be declared saints, as well as such holy women as Genovefa of Paris, but Europe's bishops were constantly finding new ones! Cemeteries outside of town (where the Romans had always put their dead, as discussed here) were as full of bones as were the catacombs. A few visions would identify a set of bones as someone who had been martyred back in the second or third century while trying to spread Christianity, and once the bones started working miracles, their identity was proven.
Soon churches began being dedicated to saints, as they had not been earlier, and all churches needed relics, bits of bone of a saint, although in some cases a piece of clothing might do. The cathedral of Chartres, for example, had the "chemise" of the Virgin Mary, the nightgown she was supposedly wearing the night she gave birth to Jesus.
One should of course be very careful, even if one does not believe in saints oneself, in calling them "superstition," as discussed more here. Medieval people did not automatically believe in every story of a saint. Bones about which there was doubt would be scientifically tested, as for example being thrown into a fire. If they jumped back out, they were clearly saints' bones. Saints were also not some manifestation of "folk" religion, for they were discovered, validated, and promoted by the elite. They were also not polytheism in disguise, because all agreed that God gave them their power, as His agents.
Although there were some "universal" saints, like the Virgin or Stephen, who appears in the New Testament being put to death for his faith, most saints were local. They were closer to the people of the region than some universal saint, much less God (who could be frightening), more likely to listen to their concerns.
Saints could be subversive. They blasted anyone who harmed "their" churches--which usually meant the wealthy and powerful. They also provided hope--no matter how horrible you had been, if you completely changed your ways, did penance, and made restitution, saints could help you achieve salvation.