Have you ever sprayed someone with a garden hose?
If you wanted to get them good, you placed your finger over part of the tip of the hose. The water then sprayed out faster and farther. Why does putting your finger over the tip of the hose make the water shoot out faster and farther?
Because pressure equals force divided by area.
Force has to do with acceleration. In this case, our force is the flow of water coming out of the spigot and running into the hose. Assuming we don't turn the knob, our force is constant.
What have we changed? The area of the space from which the water can leave the hose. The same amount of water being pumped into the hose at the same force now has a smaller area from which to escape the hose. Because pressure equals force divided by area, when the area lessens, the pressure increases.
The hose can't expand to accommodate more water, so the water has to shoot out the opening faster. Pressure has to do with how an object will feel as a result of a force exerted on it. Because pressure causes the water to shoot out of the hose faster, it will feel harder, and it will travel farther.
It's similar to what happens if you were to say hit someone at the same force with two very different objects, a textbook and a stickpin. Which one would hurt more? The pin, no doubt. Because the lesser the area, the more concentrated the force is and thus the more piercing the pressure.