The Chi Squared statistic is used in 3 cases:
Test of adjustment
It allows to test if one distribution or more is adjusted to other distribution.
This is a non parametric test, meaning that it can be used even with non normal distributions.
For instance, you can check if one distribution is similar to a normal distribution.
Test of variance
You can used the chi square to test the confidence interval of the variance of a normal distribution
Multiple test of adjustment
You can check among different groups if they are similar or different