A trade publication, unlike a consumer publication, covers a specific industry for people who work in that industry. Trade publications therefore cover an industry in more minute details than a consumer publication might. The idea is that trade publications deliver information that's of value to those who work in a certain field, but might not be of as much interest to the general public.
For example, someone who likes movies might read a consumer publication like Entertainment Weekly because it covers entertainment. But someone who works in the movie industry will probably be reading publications like Variety and The Hollywood Reporter, two trades that cover deals and other things happening in Hollywood more closely.