One-way analysis of variance (ANOVA) is used for many things in the social sciences. The basic point of using ANOVA is to try to determine whether two or more groups actually differ from one another in terms of one variable. In one-way ANOVA, we examine the effect of one variable on one other variable. Let's look at an example to show what this means.
Let us say that we look at people who graduated from a given college with degrees in two different subjects. Their major will be our independent variable. We want to know if their major had an impact on the amount of money they are making 5 years after graduation. We first take the mean salary for each group. They will almost certainly be at least somewhat different. But is that difference statistically significant? That is what we use one-way ANOVA for--to determine if there really is a statistically significant difference between the two groups.