Toilet paper dissolves as water weakens bonds between its cellulose fibers. Toilet paper is made with short wood fibers with weak bonds that break apart easily when saturated with water.
Toilet paper manufacturers work to develop toilet paper that is strong when wet while being used and yet still dissolves easily so that it does not clog plumbing. The key to quality toilet paper is choosing cellulose pulp with short fibers. The short fibers initially have a strong bond with each other. They bond together in long chains through polar attraction. This bond holds up during normal usage.
After the paper is in the toilet bowl, it becomes saturated with water. The water molecules are also polar and are attracted to the ends of the cellulose chains. The water molecules work their way between the cellulose bonds, weakening the paper. Ultimately, the bonds break, and the paper dissolves. Because toilet paper is made with short cellulose fibers, it dissolves into very small bits. These tiny, broken-down pieces move through plumbing easily and do not cause clogs.
Water only dissolves the paper into its individual cellulose fibers. It does not change the actual chemical composition of the paper. Dissolving the cellulose fibers requires an acidic solution, such as sulfuric acid.