Dear {Mr./Mrs. Name},
I am so sorry that I forgot about {a date/a meeting/an exchange/a favor}! I cannot believe that I was so scatterbrained. It's no excuse, but I hope that you understand that this week has been horribly busy due to {reason}.
I feel awful that I inconvenienced you like that and it would make me feel a lot better if I could make it up to you. Can I {take you out to lunch/give you a discount/make you a present}? It would really make me feel like less of a thoughtless jerk.
Sincerely,
{Sender}
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