Ryoma is the eldest son of the house of Hoshido, and will be king. In fact, because of the loss of Queen Makoto (Corrin's mother) his ascension is assured. In two of the games even, by the end, they show his ascension to the throne.
Despite this, Ryoma still strives to prove himself worthy of the throne. At times pushing himself beyond what he should in order to prove his worth of the title he'll soon inherit. You'd think this would likely make him a bad brother, but in fact, Ryoma knows just about everything about his siblings. Including Corrin. And is proud to support them no matter their endeavor.
In battle, he wields a powerful lightning katana, and is easily one of the most powerful units in the game when you control him. If you choose Hoshido, if will be your rock on your team. And in Revelation, he will be the unit you crave to get as soon as possible.
Above all else, Ryoma is about protecting his family and his kingdom, and heaven help you if you try to take either from him.