Hi Niwantha!
Great question. This is a way of setting a due date or deadline. So, if someone says, "Please submit your report today at the latest." they mean, "Today is the latest you can give me the report." This means that tomorrow would be too late.
Yes, you can say, "tomorrow at the latest" or any day. For example, you could say, "Submit your report by the 16th at the latest." or "Wednesday at the latest." or even "12:00 PM at the latest." All of these examples have a similar meaning: whatever day, date, or time is used is the latest day/time that something can be done or accepted without negative consequences.
Hope that helps!