It is all about pressure. When you plug upon the nozzle, there is no way for the pressure of the fluid to rise above a certain value, so pushing in is opposed by the fluid pushing back on your finger, it gets hard! However, if you open the valve and allow fluid to squeeze out, then the pressure can be relieved a bit and that allows you to keep the piston moving down. That is applying an unbalanced force that allows the fluid to accelerate from zero velocity inside the barrel to some higher velocity through the nozzle.

This is about pressure - the air inside of the syringe takes up some volume and exerts pressure on the plunger. If you keep the air inside from escaping by holding the nozzle closed, then the air will get concentrated to higher pressure as you push in the plunger - until the pressure inside the syringe is the same as the pressure you're putting on it with the plunger, at which point you can't push it in anymore, because the air pressure becomes stronger than your finger.

To simplify things, let's talk about the case of an "empty" syringe (a syringe with just air in it). Normally air is expelled from the nozzle of a syringe when we push the plunger in (if we don't block the nozzle). But when we block the nozzle, we don't allow air molecules to be expelled. To get an idea of what this implies, let's look at the ideal gas equation: PV = nRT. Even though our gas is not technically "ideal" it will still follow the basic proportionalities of this law. When we don't allow molecules to escape, we are holding "n" constant -- the number of moles of gas in the container. R and T are also constant. However, by pushing the plunger in, we are trying to reduce the volume (V) of the container. This means that the pressure (P) has to increase in order for the right hand side of the equation to be constant. Pressure is equal to a force over an area. So when the pressure increases, the force of the molecules bouncing walls of the container (including the plunger) is also higher. This means it takes more force on our part to push against these air molecules. So it gets harder for us to push the syringe in when there's higher pressure!

When you put your finger over the nozzle, you prevent any air from entering or leaving the syringe. Because the air cannot escape from inside the syringe, when you then try to push in the plunger, the air inside the plunger is compressed into a smaller volume. This creates a higher pressure inside the syringe. This higher pressure pushes outwards against the plunger, which is why it becomes much harder to push the plunger further into the syringe.