A complex sentence contains a main clause and a subordinate clause.
Jack went swimming although the water was cold.
The main clause makes sense on its own.
Jack went swimming although the water was cold.
The subordinate clause begins with a connective and does not make sense on its own.
Jack went swimming although the water was cold.
Sometimes order of the clauses can be changed so that the subordinate clause is at the start of the sentence. In this case we need to use a comma to separate the clauses.
Although the water was cold, Jack went swimming.
Starting a sentence with the subordinate clause can make writing more varied and interesting.