The Mann-Whitney U is of the most well-known non-parametric significance tests (see Mann-Whitney U). It is useful for looking at differences in the average between two groups when the variable being averaged is either ordinal only or inadequately normal - for example, looking at the difference in satisfaction ratings between two restaurants. It is also quite robust with respect to outliers.
If you want to look for differences between multiple groups, the Kruskal-Wallis H is required. If your data is numerical and normally distributed, and N at least 20, you may be better using the independent t-test.
Because the Mann-Whitney U is based on order rather than value, the output table displayed by SOFA shows the median instead of the mean.
The p value tells you how likely the difference observed would occur if drawing from the same population (i.e. where the groups didn't really have a relationship with the value being averaged). A small p value tells you that it would be rare to observe such a difference if the group doesn't have a relationship with the value being averaged. From this we might reject the null hypothesis in favour of the alternative hypothesis - namely, that there is a difference according to the grouping variable.
In the example below (based on false data for illustration only), we shouldn't be surprised the p value is very low. It is possible to see a large difference in average age and N is reasonably large for each group. The average rank is also clearly different. In this case we could reject the hypothesis that nation has no relationship with age.
Be aware that there is a certain sensitivity about terminology around this area. According to a widespread convention, we shouldn't conclude that there is a relationship, only that we reject the null hypothesis (see Hypothesis testing). We might go so far as to reject the null hypothesis in favour of the alternative hypothesis. See Statistical hypothesis testing.
U is based on the results of matches between the two groups. In each match, the winner is the one with the highest value (in a draw, each group gets half a point which is why U can sometimes end in .5). The further the number is away from an even result i.e. half the number of possible matches the more unlikely the difference is by chance alone and the more statistically significant it is. See it explained on Youtube: The Mann-Whitney U test
A video is available showing how to do the Mann-Whitney U test using SOFA Statistics: https://www.youtube.com/watch?v=Zvg1Bl852EQ&feature=relmfu