Follow the Link and its references (Especially the book by Gilbert, R.O. 1987). You will find the explanation with workout example. If you can not manage the book, send me an email. I will try to send a scanned copy of this section for you.
The Mann-Kendall test tells you if any series of dimension J has a significant monotonic tendency or not. It is quite useful to detect any possible trend and also if a break point (or several if the test is applied to part of the series) affect the series. Attention, the test is not adapted to detect any non-monotonic trend. Pay also attention if any tie is present in the series since some corrections must be applied to the computation of the variance to determine the statistics to be tested. The Sen's slope tells you the slope of the linear tendency of your series.
Use the package 'modifiedmk' in R for modified Mann-Kendall test by Hamed and Rao, Yue and Wand, Pre-whitening, Trend-Free Pre-Whitening, Sen's slope and Speraman's rho calculations