JMP output can be rather verbose at times. But you do not necessarily need all of it. I will use the same example for my explanation.
The MCA bi-plot shows you all the levels of each variable to understand the nature of the association between variables. The chi square value is a distance measure. So there is no good or bad chi square. There is no threshold for comparison. It is just information. The idea is that you might first decide if an association is statistically significant and then investigate the nature of it with MCA. MCA is interpretative.
Let's say that two variables are strongly associated. In what way? The MCA plot tells you. Your original categorical variables are re-cast into a continuous measure of distance from the centroid of all the data. Think of centroid as the average row in your data table. The each new distance measure defines a new dimension or axis. These dimensions are orthogonal as you would expect for Cartesian coordinates. Each dimension represents unique information from all the original categorical variables. These dimensions are ordered in descending inertia. Think of inertia as the total distance from the centroid in one dimension. (The symbol for inertia is the lower case Greek lambda.) The first dimension therefore maximally separates the levels. The second dimension separates the levels less than the first but more than the remaining dimensions, and so on. So the first two dimensions show you the most information about the association.
Start with one variable, such as sex. Notice that the male and female levels in your plot are well away from the origin in opposite directions along the second dimension, but they are close along the first dimension (i.e., close to 0). Now look at another variable: country. The American and Japanese levels are well away from the origin along the first dimension but close to 0 on the second dimension. On the other hand, the European level is close to 0 on the first dimension but quite negative in the second dimension. You can assess both the direction and distance away from the origin for levels of the same variable.
Now consider two variables at a time, such as country and size. The general association between these two variables can be seen as Japanese with Small, American with Large, and finally European with Medium. You can only assess direction away from the origin for levels of different variables.
