From what I understood, [allele frequency spectrum][1] is everything that concerns the frequency of all of the alleles studied in a population. It can be estimated with Tajima's D, theta, etc. 

But how is it different from the *joint* allele frequency spectrum? 


  [1]: https://en.wikipedia.org/wiki/Allele_frequency_spectrum
Joint allele frequency spectrum is allele frequency distribution calculated between two\three populations. Imagine a 2D plot, where on x axis is AFS of population 1 and on y axis is AFS in population 2. For example, you can plot derived allele counts in Yoruba versus Central European population.  Let's say, you count allele A x times in Yoruba and y times in Central Europe, then you plot it on 2D space. For three populations it will be a 3D plot.  Upscaling this to a higher number of populations is computationally very hard. 
Joint AFS is informative about migrations and other parameters, because changes in jAFS will reflect changes in demography.

Take a look at this paper by Gutenkunst et al http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1000695   