If I understand your question correctly you are asking why QIIME does rarefactions at 10 seqs/sample, then 23454 seqs/sample, then 46898, etc. The reason is that the purpose of the rarefaction curve (also known as an accumulation curve) is to see if you have adequately sampled the diversity of your samples. So, at increasing depth (larger numbers of seqs/sample) we should hopefully see the rarefaction curve level out; in other words, we should see that the amount of additional diversity we are getting by sequencing 100,000 vs 50,000 seqs/sample is not very much. This implies that we have adequately sequenced our community.
The rarefaction process is random sampling without replacement. So, depending on which sequences the computer picks, the information can be different. Repeating 10 times ensures that we are getting a more true estimate of the actual alpha diversity at that level of rarefaction.