When we project onto the therapist, for example we react to them 'as if' they were someone from our past, that is tranference. We transferred those feelings from the initial experience and person onto the present experience and person.

If a therapist reacts to the patient the same way, it is countertransference. If the therapist finds him/herself feeling anger because the patient is being demeaning and that anger is coming from the therapist's past experience of his parent being demeaning, then that is counter-transference. The therapist is reacting from his past experience and person and no longer being therapeutic. So the therapist who has had his/her own psychotherapy/psychoanalysis and knows him/herself well, is more likely to be aware of the counter-transference right when it happens and hopefully before it affects the therapy.

Simple transference happens every day. The best example I know is seeing an older gentleman at the grocery store who reminds you of your favorite and kind uncle, so you immediately have warm and kind feelings about this gentlemen, who in fact you know nothing about. The feelings (and attributes) for the person from the past have been transferred to the person in the present.