The Advisor pods are large white synth ships about the size of a tank, capable of controlled flight and marked with a registration number printed on the side. The inside is lined with cushioned walls and contains a "blanket" for the Advisors to be wrapped in, most likely some form of life support or protection from shock.
They are first seen inside the Citadel when Gordon and Alyx watch as a Pod is transported up with an Advisor tucked inside. Below the same room, several Pods are stored, many of which can later be seen fleeing from the Citadel just before it explodes.
An Advisor Pod can be seen being transported on an Advisor Platform along with a battalion of Combine soldiers and Striders. Later, another pod with the 314 URB-LOC 0017 registration code is seen crashed near where the Barn Advisor is found.