Do you mean the little button with the hand on it from your notification window?
I'm not sure if this is your question, so please forgive me if this answer isn't what you are looking for. But...When the button is brown (or gold) it means the neighbor has offered you help within the last 23 hours, and when you help that neighbor you will receive a bonus of tools as well as the usual coin reward. When the button is green it indicates that you will be the first to offer help and will receive the coin reward only.