Finned Tubes is applied for transferring heat from a hot fluid to colder fluid through a tube  wall

The rate at which such heat transfer can occur depends on three factors:

(1) the temperature difference between the two fluids

(2) the heat transfer coefficient between each of the fluids and the tube wall; and

(3) the surface area to which each fluid is exposed. In the case of a bare (unfinned) tubes, where the outside surface area is not significantly greater than the inside surface area, the fluid with the lowest heat transfer coefficient will dictate the overall heat transfer rate.

When the heat transfer coefficient of the fluid inside the tube is several times larger than that of fluid outside the tube (for example steam inside and oil outside), the overall heat transfer rate can be greatly improved by increasing the outside surface of the tube. 

In conclusion, finned tubes is to increase the outside surface area of the tube