An intermediary is a person who passes information between two other persons or groups. These other persons or groups are usually not in contact with each other. If you had a friend (call her Kat) who knew a person (call her Anne) who was selling jewellery that you wanted, then you could ask Kat to tell Anne. Kat is then an intermediary. Intermediate is a step in a process or action, it is not a person. There can be many intermediate steps between the beginning and end of a process. Think of wheat, there are many intermediate steps between planting wheat an eating bread made from wheat.