"Notwithstanding the foregoing" means in spite of what was just said or written. The word "notwithstanding" means in spite of or despite. The word "foregoing" means what has come earlier.
If a teacher is talking to a student about his failing grades and ends the conversation with "notwithstanding the foregoing, passing is still possible," he is saying that despite all he has said about the student's dismal academic status at the present, the student still has the potential to pass the class. "Notwithstanding the foregoing" is a transitional phrase that indicates the speaker or writer is about to give a different spin on a situation.