This is a polite apology for causing someone to wait. "お待たせして" (omatase shite) is a humble way to say "having kept you waiting." It's appropriate to use when you've been delayed, for example, if a customer has waited for service, or if you've arrived late for an appointment.

相手を待たせてしまったことに対し、丁寧に謝罪する際に使う言葉です。