A medium is a communicator between worlds --they mediate between the physical world and the spiritual world. Most often, mediums can talk to those who have crossed over (yes, we can smell, hear, and "see dead people"). In many instances, we can often share messages from your Angels, Spirit Guides, and other higher dimensional beings. We act in a capacity delivering messages and assisting in communications-- we are the middle women & men to deliver the messages only ...not to interpret them.
Mediums exist in nearly every culture. Some allow the energies to use their bodies to share messages --called channeling-- while others (myself included) agree just to receive said messages and delivery them, we while maintain control of our bodies. The Spiritualist movement brought mediumship to the forefront of American consciousness in the late Victorian era. Even the well known Harry Houdini and Mary Todd Lincoln participated in their day.
Séances are formal gatherings where mediums share these messages and bring closure and connections from loved ones who have crossed over. My own séances (I call them "Peeking Through the Veil") do not reflect traditional practices of sitting around in a circle holding hands looking into a crystal ball, but they do give a forum for group participation in sharing messages from the Other Side of the Veil.
Mediumship, in all forms, brings many miracles. Watch the Afterlife Investigations: The Scole Experiments to learn more about how modern day mediums practice their gifts. But know... even some of that intense contact with the Other Side, while incredibly cool, still keeps me awestruck.