They are very similar to D&D. Each stat will have dialog affects, but they will also affect your performance in your majors as well. Day 3 once released will give a bit more information on how the courses work and you'll be trying to balance grades, relationships and other aspects as the game progresses. The majority of this mechanic won't be seen very early on, but will have an affect that lasts throughout the playthrough.
Also, some stats may play an unexpected role in some majors depending on your score in them, for instance, if you were in the mage major and had both a high intelligence and high strength or something like that it may unlock different options later down the road. However, the main stats that will affect your courses in the major are as below:
Fighter - Strength
Mage - Intelligence
Holy Arts - Wisdom
Guardian - Charisma
Rogue - Dexterity
I don't intend for there to be extremes that only min/maxers can attain, but people are creative and enjoy building characters in different ways so there may be some that try to attain a "perfect" score.