What force helps us row a boat?

To make this as simple as possible, let's consider the boat and the rower to be one object. When we do this, there are two main forces acting on a boat as it is rowed: The force of the water pushing on the spoon (sometimes called an oar), and the force of the drag due to the fluid friction of the water on the boat.

Newton's 3 Laws of Motion are all apparent in the motion of the boat through the water, and a brief summary of those laws is necessary to discuss how these forces affect the boat. 

Newton's 1st Law states that an object in motion will stay in motion and an object at rest will stay at rest unless acted upon by an outside force. This means that the boat will just stay put unless a force is applied to it (by rowing), and once it's in motion, it will stay in motion unless a force is applied to it (by drag from fluid friction).

Newton's 2nd Law states that F = ma. This means that when a force is applied to the boat and rower it will result in an acceleration. This acceleration can be either a speeding up or slowing down in the speed of the boat. The force of the water pushing on the spoon during rowing will make the boat speed up, and the force of the drag will cause the boat to slow down. If you draw a free body diagram and do the calculations, the force of the water pushing on the spoon during rowing will be positive, resulting in a positive acceleration (speeding up), and the force of the drag will be negative since it's in the direction opposite the motion of the boat, resulting in a negative acceleration (slowing down). 

Newton's 3rd Law states that for every action there is an equal and opposite reaction, meaning that when the spoon is moved against the water, the water is pushing back against the spoon, causing the boat to move forward.

Let's consider the rower and the boat to be two separate objects for a minute. Another important point is that static friction between the rower's backside and the boat is causing the rower to stay still, so the boat moves. Imagine the difference we would see if the rower were sitting on a skateboard and trying to row! That static friction between the rower and the boat would be gone, so the rower would move and not the boat.

So, to help row the boat you need the force of the water pushing on the spoon, but the force of the drag is always going to be there slowing down the boat, and those are the two main forces acting on a boat while it is being rowed through the water.