How does Meiosis increase variation?

In the first stage of Meiosis 1 - Prophase 1, after the chromosomes have coiled and condensed they ay touch each other at points known as chiasmata, and Crossing Over occurs. This is where genetic information is swapped between the pair of chromosomes. This results in a change in genetic code and thus, increases variation. 

Also, in metaphase 1 and , chromosomes are arranged by random segregation and in Anaphase I and II chromosomes are independantly separated due to this random allignment and this, along with crossing over, means that the genetic code in each of the 4 haploid cells formed is different, thus creating varied cells. 

Another way meiosis allows variation to happen is because during interphase, when DNA is replicated, mutations may occur, meaning the genetic code differs from that of the parent and so their DNA has changed.