Multivariate analysis of variance (MANOVA), and analysis of variance (ANOVA) tests are statistical methods for analyzing the difference in means between variables. The MANOVA and ANOVA tests are similar in nature to one another, because they work on the same assumptions; however, there are some key advantages to using a MANOVA over an ANOVA test.
Multiple Dependent Variables

The MANOVA can measure multiple dependent variables, while the ANOVA only allows for one. The ability to measure the effects of an independent variable on multiple dependent variables is useful for comparing the effect of the independent variable in different settings. You would need to run multiple ANOVA tests to measure the same number of things that one MANOVA does.
Simultaneous Testing

Because the MANOVA tests multiple dependent variables at once, you're testing the effects of the independent variables simultaneously. Running multiple ANOVA tests on each variable not only takes more time, but increases the risk of type I statistical errors. A type I error occurs when a statistical test rejects a null hypothesis when it is true. For example, if your null hypothesis is "students who study have higher test scores than students who don't study," then a type one error would cause your results to reject that statement, even though your data actually supported it.
Finding Effect

The MANOVA also increases your chance of finding an affect that an independent variable has. When you're measuring the independent variable's affect on multiple dependent variables, you may find that there is a significant influence on one of the dependent variables, but not the others. Using an ANOVA, you would have only been testing one of the dependent variables.
Disadvantages

Although MANOVA tests have significant advantages over the ANOVA, there are also some key disadvantages. The test is more complex to run than a single ANOVA, and your results can be more ambiguous. For example, if you find that an independent variable affects multiple dependent variables, you can't tell for certain whether or not it truly was the independent variable, or the multiple dependent variables having an affect on each other. Because ANOVA tests only have one dependent variable, the results are clearer.