This is just another word for “the news” except it only pertains to news sources specific to the entertainment industry. You’ll often hear people say, “Did you read about it in the trades?” or “Saw you in the trades the other day. Congrats!”.
When people mention the trades, they are usually referring to one of three major entertainment news sources.
http://www.variety.com (also available as a weekly newspaper subscription)
http://www.hollywoodreporter.com (also available as a weekly newspaper subscription)