The main question R'MES addresses is "does this motif occur in that biological sequence with an expected frequency?" In other words, can we observe it so many times, or so few times, just by chance? Usually, when the answer is no, such a motif is a candidate to have a particular biological meaning; only a candidate: statistical significance is not equivalent to biological significance.
A brief presentation of the statistical method used in R'MES to evaluate the significance of a motif frequency in a sequence can be found in the user guide. For more details about the methodology, please refer to the following tutorial (pdf) or to the book DNA, Words and Models by Robin, Rodolphe and Schbath published by CUP in 2005 (or by BELIN in 2003 for the French version).
If you have been using R'MES or if you want to refer to R'MES, please mention the following reference:
Schbath, S. and Hoebeke, M. (2011). R'MES: a tool to find motifs with a significantly unexpected frequency in biological sequences. In Advances in genomic sequence analysis and pattern discovery (L. Elnitsk i, O. Piontkivska, and L. Welch, eds.). Science, Engineering, and Biology Informatics, vol. 7. World Scientific.