I came across this technique when dividing complex/imaginary numbers. When you use the technique on those numbers, it actually simplifies them. I tried using the technique on regular fractions and noticed that it does not change the original fraction. I'm going to assume it doesn't change the value of the complex fractions either, but somehow "re-phrases" them.
You are NOT multiplying the "fraction by its conjugate". You are multiplying BOTH the top and the bottom of the fraction by the same complex number. That is equivalent to multiplying the fraction by 1, which does not change its value.
For example, if you want to simplify (3+2i) / (4+3i) you would multiply both top and bottom by (4-3i). This is the same as multiplying the fraction by (4-3i) / (4-3i) = 1.
The reason this simplifies the fraction is that when you multiply a complex number by its conjugate the imaginary parts cancel out leaving you with a real number. So, you end up with a real number on the bottom of the fraction, which you can distribute to the two parts of the top.