The Wilcoxon Signed Ranks Test (see Wilcoxon signed-rank test) is useful for looking at differences in two variables. The data must be paired e.g. looking at pre and post-diet weight. The variables being averaged must also be measured at an interval level of measurement.
If your data is numerical and is adequately normally distributed, you may be better using the paired t-test.
If you are looking at independent/unpaired data e.g. height between two countries, the non-parametric equivalent is the Mann-Whitney U Test.
The p value tells you how likely the difference observed would occur if sampling from a population in which there is no actual difference. A small p value tells you that it would be rare to observe such a difference if there is no actual difference between the variables. From this we might reject the null hypothesis in favour of the alternative hypothesis - namely, that there is a difference.
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.