This analysis is appropriate when you have a single qualitative factor which divides the observed responses into different classification groups. It is used to detect a significant overall difference between the average response within different classification groups. If a difference is detected, you may also explore a breakdown of differences among individual group means.
When the single qualitative factor has only two levels, t-test results are available in addition to the usual ANOVA results.
When you have several factors that you want to investigate, the One-Way ANOVA is not appropriate; use Multiple Regression and ANOVA instead.