MANOVA is used to compare averages of two or more "dependent" variables between two or more categories of an "independent" variable.
MANOVA is conceptually an extension of ANOVA. The main difference is MANOVA can compare two or more "dependent variables" simultaneously, between two or more groups of an "independent variable" whereas ANOVA is designed to compare only one "dependent variable" between three or more groups of an "independent variable".
Continuing with the weight loss example in my previous tutorials, imagine you have a second "dependent variable", let's say systolic blood pressure. Your "independent variable" is type of diet (standard, new diet 1 and new diet 2). You want to see if either weight loss or blood pressure is different among the three diet groups.
As with the two-sample t-test and ANOVA, the complex mathematical calculations are performed by software like SPSS. The software will produce a p-value (probability value). By convention, if p is < 0.05, the sample results provide strong evidence that the average weight loss and/or systolic blood pressure are different among the three groups. Further testing would be needed to determine which dependent variables were different among the three groups.