"Appreciate" in this context means that you are thankful and grateful for what this person has done for you. (It should be easy to look up in a dictionary. If you can't find it, look up "gratitude", which is a similar concept.) You would use this phrase if someone has actually supported you and you would like to thank him or her. For example, if he or she: - Gave you money (financial support). You would especially use this phrase if you are representing a charity and they have given a donation. - Gave you encouragement (emotional support) when you needed it. You would not use this phrase if you are asking someone for support and they have not yet given it. It would seem like you are trying to make them feel guilty if they can't give you something. If they bought something from you, you would want to thank them for their purchase, but you should then say that you hope they will enjoy what they bought. (More focus on the customer, less focus on you.)

Appreciate in this context, means that they have thought a lot about your support and feel that it is of great value, that it was really good of you to give the support, that it was needed and that it helped.