It can be used in different contexts, for example:
* To emphasize the truth of something: "Je suis sérieux, je ne l'ai jamais fait." (I am serious, I never did it.)
* To express seriousness about a topic or task: "Je suis sérieux à propos de mes études." (I am serious about my studies.)
* To signal that you're not joking: "Je suis sérieux, arrête de rire !" (I'm serious, stop laughing!)
The meaning of "Je suis sérieux" depends on the context and the speaker's tone.