Meiosis is significant for several reasons, but one of the most important is that it provides for almost infinite genetic variety. It accomplishes this by means of two related processes, collectively referred to as recombination.
Firstly, the chromosomes are "independently assorted". This rather unhelpful phrase means that when each gamete gets one chromosome out of each homologous pair, whether each chromosome comes from the maternal or paternal side is random. (As you know, you have TWO chromosome 1s, TWO chromosome 2s, etc. - homologous pairs - one from each parent.)
In other words, if we consider just two chromosomes, any particular gamete that you make could contain the chromosome 1 that came from your father and the chromosome 2 that came from your mother, OR the other way around, OR both chromosomes from you mother, OR both chromosomes from you father. For a better explanation of this, try my post here.
This process is exponential, and since we have 23 pairs of chromosomes, there are 223 possible different gametes that this process is capable of producing. This process is the result of random orientation in metaphase I.
Secondly, there is the process of crossing over. This refers to the swapping of similar segments of genetic material between homologous chromosomes. This process therefore ensures that the chromosome 1 (say) that came from your father is changed into something unique - it has now swapped a bit of itself with the chromosome 1 that came from your mother. Theoretically, this process can create 2 to the power of the number of genes you have (e.g. 230 000), which is a number near enough to infinity as makes no difference to evolution (although the actual number is less due to things like linkage disequilibrium and the fact that the process doesn't ever happen 30 000 times per gamete!).