(a) in what way is the equator different from all the other parallels?

(b) the equator gets uniquely used in the latitude system in what way?

Answers:

Firstly, we have to define what parallels are:

They are imaginary horizontal lines that never touch (that is why they are parallel) that travel across the Earth globe from East to West, forming circles that become smaller and smaller as they get closer to the poles.

Now, the equator is also a parallel, whose latitude is , however, what makes it especial is that this line is in middle, dividing the Earth in its two hemispheres: Northern hemisphere and southern hemisphere. In addition the radius of the circle it forms is the greatest of all the parallel circles in which the Earth was divided  by geographers.

As explained in the first answer, the equator divides the Earth in two hemispheres and this is useful to find the latitute.

In this sense, latitude is defined as the angular distance between the equatorial line and a specific point on the Earth. Dividing the planet in the northern hemisphere and the southern hemisphere, depending on the location of the geographical point with respect to the equator.  

So, the parallels allow us to determine the latitude of a point, in other words, they help to know if the position of a point is North or South of the Equator.