Meaning : A struggle (usually prolonged) between competing entities in which neither side is able to win.
Example :
The hope that his superior campaigning skills would make a difference evaporated in the realization that electioneering had become a form of trench warfare.
Meaning : A type of armed combat in which the opposing troops fight from trenches that face each other.
Example :
Instead of the war ending quickly, it became bogged down in trench warfare.