When writing with a nib and wet ink, one could either wait for the ink to dry before folding the sheet or putting other sheets on top, or one could use blotting paper to absorb the excess ink. (The blotting paper might finish up with a copy of the text, in reverse of course, and this formed the basis of a clue in many detective stores). The rolling blotter held a piece of blotting paper in a curve, such that it could be rolled down onto the wet writing.
This is based on a picture found on the Internet, offering a blotter for sale. In the original, the body is mahogany and the top is silver(-plate), embossed with, if I remember correctly, bas-relief portraits of Goethe. It is 2.25" wide, 5.5" long, and the wooden roller is 1.5" deep.
From the left: