The Speaker can allow any MP to make a personal statement. They are usually related to conduct. For example, if the Standards Committee recommends that an MP make a personal statement for having breached the Code of Conduct, the Speaker will generally allow this.
If the Speaker has agreed that you can make a personal statement, you must clear the text with the Speaker in advance, and must stick to that text.
Personal statements are made after Question Time and any urgent questions or oral statements. The annunciators (the monitors around the parliamentary estate) will show that a personal statement is taking place.