What happens when many water molecules come into contact with one another?

A water molecule consists of two atoms of hydrogen linked by covalent bonds to the same atom of oxygen. Atoms of oxygen are electronegative and attract the shared electrons in their covalent bonds. Consequently the electrons in the water molecule spend slightly more time around the oxygen atomic center and less time around the hydrogen atomic centers.

They form hydrogen bonds with each other.
The electronegative oxygen bonds to electropositive hydrogens on other molecules. This intermolecular attraction is what causes water to have such a surprisingly high boiling point, what causes it to expand on freezing, what makes it such an excellent solvent for polar molecules, etc.