This situation may mean that boys are expressing their love or confession to girls, or promising or guaranteeing the importance or authenticity of something to girls. The specific meaning depends on the context and specific situation.
For example, a boy said to a girl, "I'm serious, really!" " I like you. Do you want to be with me? "So what he means is that he really likes this girl and asks her if she wants to be with him.
If a boy says to a girl, "I'm serious, really!" " I will always support you and help you realize your dream. "So what he means is that he supports and loves this girl very much and is willing to help her achieve her goal.
In short, "I'm serious, really!" Usually a sincere and firm tone indicates that the speaker's attitude and feelings are very serious and true.