Translation:I am sick today.
了 is here to show completion - "getting sick" has been completed even tho you are still ill. In English we don't think of it like that for today, but we're not just learning one phrase here. Change it to yesterday or last week and "became / got sick" makes more sense.
I have the Impression that the Chinese pronunciation should be a little bit more clear in a course for learners ... - I have the Impression that the speaker try to speak "very realistic", but this is not helpful for persons who try to learn. A bit slower and clearer would be helpful. The "了" in this example is nearly not to recognize. Even if a lot of people in real life speak like that, I would like that for teaching the pronunciation is "classical". Thank you for improoving that.