Basically just for appearance.
Titanic was the largest and most powerful ship at the time and it could get away with only 3 funnels but they thought if it only had 3 it would make it look less impressive compared to ships like the Lusitania and Mauretania (who were owned by Cunard. White Star Lines rival). In the movie Rose (Kate Winslet) mentions how Titanic doesn't look any more impressive than the Mauretania. That was coming from her being a bit of a spoiled rich girl and not knowing anything about ships. Titanic was actually much bigger than the Mauretania (in red)
The funnel at the back on the titanic is the dummy one. Titanics engine is actually located right between the 3rd and 4th funnel. When I said it was not functional that was a lie because it was used for ventilation of some areas on the ship like the baths, smoking rooms, etc. so steam/smoke did come out of it but not the kind of dark smoke you'd see from burning coal!