Respond to what is said
Talking about what has been said is the best way to clarify exactly what the person giving you feedback means. It is also a good way to show that you have listened to and appreciated what they have said. You may be able to immediately discuss any development opportunities that would help you improve the skill being discussed.
Vocalise your feelings about the feedback
It may well be that you do not agree with what is said, or that you do not agree when you first hear it. Your mentor or mentee could have misunderstood something you said or did - which in itself could be valuable feedback about external perception of you. If you accept the feedback in the spirit in which it is given (hopefully a constructive one) then this will ensure the next feedback session you have is more relaxed as you are helping build a healthy relationship.
Write it down!
To get the greatest benefit from feedback you really need to think about it for some period of time after it is given. The only way to be sure your memory does not play any tricks on you is to create a written record of what is said. This need only be a few words scribbled on the back of a folder, but just ensure it is something you can refer to later.
Make time to reflect
As discussed above, to ensure feedback makes a difference to your development you need time to reflect on what is said. Finding time to sit down and just think about yourself can be almost impossible. Public transport users could use the time they spend waiting for the train or bus considering this. People who travel by car might need to book an actual appointment with themselves. Perhaps staying 15 minutes extra after work - or if this will be interrupted spending the 15 minutes after your favourite soap opera ends once a week will make a real difference.
As we mentioned earlier, you may not agree with what is said. If you find that you still do not agree after you have had time to reflect then why not ask for a second, third or even fourth opinion? You can ask your colleagues, staff or bosses to comment on the same area and see how their opinions compare. It is often useful to get this kind of 360 degree appraisal of an aspect of your performance.