Feed-forward means that the noise is measured at some “remote” location and that the measurement is used to create an anti-noise signal inside the headphone or earphone. The designer must decide in advance what happens to the noise as it moves from the remote location into the headphone and setup some signal processing based on this prediction.
Feedback means the noise is measured at the same place as the anti-noise signal is produced, i.e. Inside the headphone. There is no need to guess what will happen to the noise in future, it is being instantaneously measured and corrected.
Both styles of noise cancellation have advantages and disadvantages. For feed-forward there are problems such not being able to deal with noise getting into the headphone (e.g. Through the body) that the remote measurement does not know about, it is susceptible to wind noise pickup, that is noises measured by the remote sensor that do not enter the headphone. Feedback presents much more difficult design processes. We prefer feedback, take on the design challenge in the lab and let the user enjoy the performance advantages!