Hydrogen bonding is a special type of dipole-dipole attraction between molecules, not a covalent bond to a hydrogen atom. It results from the attractive force between a hydrogen atom covalently bonded to a very electronegative atom such as a N, O, or F atom and another very electronegative atom.
The bonds between oxygen and the hydrogen atoms within the water molecule are polar covalent bonds,i.e., the electrons are not shared equally between oxygen and hydrogen. Oxygen has a higher affinity for electrons than does hydrogen