DMS stands for dimethyl sulfate. Basically DMS is footprinting or fingerprinting if you like, of the RNA structure. It is a chemical check of which bases are paired as they should be and which are not. Rhiju describes it as doing following. DMS reacts only with unpaired A and C nucleotides. Nando explains, "DMS works by binding the Watson-Crick edge". As Brourd added it 1.5 - 3 days to complete.
Here is a science paper, the abstract do a good job of explaining what DMS is.