The subordinate clause in the sentence "The trouble was that he forgot where he put his keys" is a noun clause.
A subordinate clause is a clause that is dependent on the main clause. It cannot stand alone. The subordinate clause in this sentence is: "The trouble was that". The main clause in this sentence is: "he forgot where he put his keys". From the above we can see that the main clause can stand on its own but the subordinate clause cannot stand on its own.