When someone says
I stand corrected.
What does that mean?
It means "I admit that I was wrong".
See e.g. Cambridge Dictionaries:
Note that the Cambridge Dictionary marks this idiom as "formal", and Merriam-Webster's Learner's Dictionary as "somewhat formal".
It means, "I admit that I was wrong".
It is often used by a person who has been holding a strong opinion when faced with conclusive contrary evidence.