I'm not familiar with "multivariate multidimensional scaling", but I can explain "multidimensional scaling" some. Multidimensional scaling (MDS) is a method for taking information about how far apart some points are, and arranging them in space so that they're approximately that far apart. The points could be anything: People, images, sounds, products on Amazon, books... Anything that you could define some kind of similarity measure for.
Here's an [example](https://upload.wikimedia.org/wikipedia/commons/thumb/b/be/RecentVotes.svg/708px-RecentVotes.svg.png
) from Wikipedia.
The people who created this figure did so by taking all the members of the U.S. House of Representatives, and finding out how often they voted the same way on something. This is essentially a measure of how similar their stances are: If two representatives voted the same way 95% of the time, they probably have pretty similar stances, but if they voted the same way only 30% of the time, their stances must be pretty dissimilar. Then they applied MDS, which found a two-dimensional arrangement of where to put each representative, so that the distance between two points in that 2-D plot is as close as possible to matching how dissimilar their voting patterns are.
MDS has limits, because sometimes it's impossible to accurately capture how close/far apart all the points are in only 2 or 3 dimensions. Take, for example, 8 points that form a cube. There is no possible way to plot those 8 points in 2 dimensions so that all of their distances from each other in that 2-D space are the same as their original distances to each other.
In more "nuts and bolts" terms, MDS usually takes as an input a "distance matrix", which is a N by N matrix of numbers (where N is the number of data points you have) where, say, the 8th column of the 4th row is 'how dissimilar is point 8 from point 4'. And MDS will spit out a set of coordinates in 2-D (or 3-D or whatever you want) that roughly corresponds to how far apart those points are.