Definitions:
average in amount, intensity, quality, or degree

a person who holds moderate views, especially in politics

make or become less extreme, intense, rigorous, or violent

review (examination papers, results, or candidates) in relation to an agreed standard so as to ensure consistency of marking

(in academic and ecclesiastical contexts) preside over (a deliberative body) or at (a debate)

monitor (an internet forum or online discussion) for inappropriate or offensive content.

retard (neutrons) with a moderator