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Samples
When there are more than two samples, an ANOVA is more reliable than the t-test. The t-test can only be used to investigate differences between two means. Though multiple t-tests may be carried out to compare more than two means with each other, this can lead to sever complications. An ANOVA is a relatively simple way to compare the means of several samples.
Numbers
One of the main advantages of an ANOVA is that the number of observations in each group doesn't have to be the same. For example, an experimenter comparing the effects of drinking tea on health might be able to find 100 non-tea drinkers but only 96 tea drinkers.
Factors
ANOVAs allow for experiments where populations are classified in two categorical factors. For example, an experiment might investigate the exam scores of students who are female or male -- the first factor -- and either have or have not had home additional home schooling, the second factor. ANOVAs analyzing two-factor experiments are known as two-way ANOVAs. They remove some of the random variability and allow the experimenter to look at the interactions between factors. They also allow experiments with a smaller total sample size, as two things are being studied at once.
Assumptions
Before an ANOVA is applied, the experiment must satisfy some methodological criteria in order for the results to be valid. The population involved in the sample must be normally distributed, meaning that it must be a fair representation. Variances of the population must also be equal. Samples used in the experiment must be independent, and each level of the factor must be applied to a sample.