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In manual exposure mode, the aperture and shutter speed are both set by the photographer, and these exposure settings combined with the camera's ISO or film speed determine how the background (ambient lighting) is exposed. The subject, however, can still be illuminated by the automatic flash metering system since the flash will automatically calculate output levels using TTL or E-TTL metering.
This is how flash works in manual mode. Note that this means the manual exposure mode setting only, which can use automatic TTL flash metering (it will not use A-TTL metering in manual exposure mode). Also, it doesn't refer to setting the output of the flash manually—that's manual flash and a different topic altogether.