Imagine we have a beaker with a maximum capacity of 100 milliliters.  If the metric system bugs you, then think of a pail that can hold 100 ounces or 100 cups, or a barrel that can hold 100 gallons. Let's suppose that this container is plastic, to allow us to cut it easily.
	Let's fill it with 50 ml (or oz, cu, gal, or whatever) of water.  You would say it is half filled, or you could also calculate that it is: 50ml / 100ml x 100% = 50% filled. The same thing happens with Relative Humidity.  RH is calculated by taking the actual amount of water present in the atmosphere (the Specific Humidity), dividing it by the maximum capacity of the atmosphere (the Saturation Specific Humidity), and multiplying by 100% to turn that fraction into a percentage.
	If we cut off the top of this container (that's why we made it out of plastic, to cut easily) so that it has a maximum capacity of 75 ml (or whatever units you want to make it), then, even though the same amount of water is present, you would say that it is 50ml / 75 ml full, or 2/3 full.  You could also say that it is: 50ml / 75ml x 100% = 66.7% filled.  Even though the amount of water in it hasn't changed, it is closer to being filled, just by changing the size of the container. A similar thing happens when we decrease the temperature in the atmosphere.  Even though the same amount of water vapor (the Specific Humidity) might be present, the CAPACITY of the atmosphere to hold that water vapor (the Saturation Specific Humidity) decreases, which increases the Relative Humidity.
	Let's cut off more of this container, so that it now can hold only 60 ml.  Again, even though the same amount of water is present, you would say that it is 50ml / 60 ml full, or 5/6 full.  You could also say that it is: 50ml / 60ml x 100% = 83.3% filled.  Note that as the size of the container decreases, the container is closer to being filled, without changing the amount of water. The analogy to the atmosphere is that we continue to decrease the temperature so that the Saturation Specific Humidity continues to decrease.
	Now let's neatly cut off the top of the container so that the maximum capacity is exactly 50 ml.  The container is exactly filled, and we can calculate that it is: 50ml / 50ml x 100% = 100.0% filled.  It is completely filled, just by reducing the volume of the container. This is what happens in the atmosphere with respect to water vapor.  As you decrease temperature, the carrying capacity of the atmosphere for water vapor (the Saturation Humidity) decreases.  This is what you see in the graph of Saturation Humidity vs. Temperature.  As temperature decreases, eventually, you reach a point where the Specific Humidity = the Saturation Humidity, and you are at 100% Relative Humidity.  The temperature where this occurs is known as the "Dew Point".
	Suppose we now cut the container down to 30 ml.  Is that 50 ml of water going to stay there?
	Of course not.  What will happen is that 20 ml of water will spill out over the sides, and the container will now hold the maximum amount it can hold.  How full will it be? 30ml / 30ml x 100% = 100.0% It will STILL be 100% full, but with less water than it used to have.  Every time you decrease the size of the container, the amount of water in it will decrease but it will REMAIN FULL.
	This is what happens in the atmosphere as temperature decreases.  The Saturation Specific Humidity (the "size" of the container) decreases as temperature decreases.  When the Saturation Specific Humidity reaches the Specific Humidity (the amount of water actually present), any further temperature decrease will cause water vapor to condense ("spill out" of the atmosphere), and you will get dew, fog, mist, or cloud formation (and eventually precipitation), depending on where in the atmosphere you are (on the ground, near the ground, or higher up). The temperature at which the Saturation Humidity reaches the local Specific Humidity is called the "Dew Point", and any further temperature decrease will cause condensation.

I've prepared a Youtube video (link below) on the calculation of Relative Humidity.  This has a direct application to the Humidity Quiz and Investigation assignments that you'll be doing, so please watch this video!

Calculation of Relative Humidity