The Mann-Whitney test is a nonparametric equivalent to the 2-sample t Test. It tests the hypothesis that the medians of two distributions are equal. The assumptions of the test are that the distributions are the same shape and have equal variances.

You did not provide enough information on your experimental design to tell whether this is the best test. There are also the Kruskal Wallis and Moods Median tests, which are nonparametric equivalents to 1-way ANOVA.