I met her today. (The meeting between the subject and the object happened sometime earlier today.) I have met her. (We do not know when the subject met the object.)
You mean that meeting her is is pat of your experience of the day so far. With punctual activities such as 'meet', the present perfect is less common than the past simple with specific time periods in affirmative statements, though more common in negative ones.The act of meeting somebody is short, and is therefore likely to be presented as a past-time action. The state of not-having-met (yet) ext