a chi-square test indicates whether there is anything different than the "expected" count of data points in each cell of a crosstabs table. What the expected count is depends on what kind of chi-square test you are using.
For example:
If the entire sample is split 60/40 for women to men, but when you split by age group there are: 80/20 for the younger participants and 50/50 for the older participants, then the chi-square statistic for the Age-by-Gender analysis would likely be significant. That is an over-simplification, but that is the general idea.
In layman's terms, what does a chi-squared test tell you?