"Dry", or Anhydrous refers to the level of water in the solvent. Dry solvents are usually very low water percent, and they are used in reactions that are very water sensitive.
For example, Histological Grade Methanol 98% has total impurities of <0.5% water
Or, Anhydrous Methanol has total impurities of <0.002% water
Wiki has a little blurb about anhydrous solvents, nothing huge, but enough to explain the basic idea.
EDIT: Sorry I can't be more help on the actual reaction, but I thought I'd pipe about the dry methanol.