An independent samples t-test is a statistical method of comparing two samples in terms of their means. For example, you could compare the SAT scores of men and women at a certain university, or the heights of 12-year-old boys and girls.
Simplicity of Interpretation
The output from an independent samples t-test tells you how different the mean of one sample is from the mean of the other group. It tells you the mean of each group, and the average difference between the groups. It also tells you whether this difference is statistically significant. Statistical significance is a measure of how likely differences as large as the ones in this sample are, if the two populations from which the samples are drawn have the same means,
The independent samples t-test assumes that the two populations are normally distributed (the bell-shaped curve) and have the same variance (the variance is a measure of how spread out a distribution is). However, the t-test is fairly robust to violations of the first assumption, and there are methods for using the t-test with two samples from populations with unequal variances.
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Ease of Gathering Data
The independent samples t-test requires very little data: Simply the values of subjects from each of two groups on some quantitative variable. The t-test is valid even with a small number of subjects, and requires only one value from each subject.
Ease of Calculation
These days, even t-tests are nearly always done with the aid of a computer. But the formula for the independent samples t-test is simple, and this makes it easy to understand what is going on. This is especially appealing to people without much statistical training.