Seymour's mother wanted to become the Final Aeon for him to use against Sin so that he could win the people's love and respect after having been ostracised from the Guado community and exiled to Baaj... That's basically what we learn of Seymour in Zanarkand.

But yeah, it doesn't really make sense with the story. A summoner can't receive a Final Aeon from Yunalesca unless he/she has prayed at every other fayth in Spira's temples (minus the Stolen Fayth Cavern and Remiem), but Seymour seemed to have gone straight from Baaj to Zanarkand without acquiring any other aeons (how did they even do that? Boat?)

And then her fayth is stored back at Baaj anyway? So does that mean Seymour's mother just wanted to become a normal fayth and aeon for her son instead of the Final Aeon.. If so, why bother going to Zanarkand at all?