what is present in water molecule that allows it to react with a hydrogen ion

Water is a protonated solvent. It undergo self ionization to form hydrogen and hydroxide ions. In fact water molecule always exists in equilibrium with these two ions.

This hydrogen ion is very reactive and thus never exist in free form. It reacts with the lone pair of electrons present on O atom of water molecule to form hydronium ions i.e. H3O+.
Thus the lone pair of electrons of water molecules are responsible for its reaction with hydrogen ion.