Outlook is your mail client. Your actual mailbox lives elsewhere. It is your mailbox host we need to understand. Without actionable clues, the community will be reluctant to help because getting you an answer can be protracted. Could you please update your submission with details such as: Is your email hosted in Exchange Online, Gmail, Exchange on premises, some other mail provider? Within Outlook if you navigate to "Account Information", part way down the page you should see "Mailbox Settings". This will indicate how much space you are consuming and how much space you are entitled to. What is the amount of space you are entitled to? If it is a tiny but round number, it is probably a misconfiguration. If it is a completely weird value, that may indicate a different problem. If its a really big number, you've probably hit a service limit. Is this a recent issue after years with no problems? If so, are you aware of any recent change? Are there any other details in the "mailbox full" message that suggest a configuration value or other cause? Do you have administrative access to your email hosting service?
With this detail, someone in the community will, hopefully, be able to better theorize about your problem and will know whether you are in a position to fix it yourself or whether you need to engage another party.