“Chi-Square test” usually refers to the chi-square independence test: a test for investigating whether there's a relation between two categorical variables.
For example, does region ‘say anything’ about marital status? In this case, a chi-square independence test will answer if the percentages of people who married, never married or divorced are the similar over US regions such as West, Midwest and so on.
The reasoning behind the chi-square independence test is explained in simple language in Chi-Square Test - What Is It?.
For testing if some hypothesized frequency distribution is likely -given your data- the one sample chi-square test is the way to go.