Hi, @amcrowell!
There are two pieces of documentation that I think will help to answer your question about those box plots.
This snippet from the alpha rarefaction plotting section of the Moving Pictures Tutorial:
This visualizer computes one or more alpha diversity metrics at multiple sampling depths, in steps between 1 (optionally controlled with
--p-min-depth) and the value provided as--p-max-depth. At each sampling depth step, 10 rarefied tables will be generated, and the diversity metrics will be computed for all samples in the tables. The number of iterations (rarefied tables computed at each sampling depth) can be controlled with--p-iterations. Average diversity values will be plotted for each sample at each even sampling depth...
And these two parameters from the docstring for the qiime diversity alpha-rarefaction command
--p-steps INTEGER The number of rarefaction depths to include between
Range(2, None) min-depth and max-depth. [default: 10]
--p-iterations INTEGER The number of rarefied feature tables to compute at
Range(1, None) each step. [default: 10]
The 10 rarefied tables mentioned in the tutorial quoted above come from the default value for --p-iterations mentioned in the docstring. For each sampling depth step, there is a box plot to help visualize the results.
Also, this forum discussion about Rarefaction and alpha diversity may be useful.
As for your second question, no that number is not in the thousands. You can check your feature-table summarize visualization to see what the deepest sequenced sample is. That way you can make sure that you set the max depth accordingly.
I hope that helps but please let me know if I can further clarify anything!