Water molecules have covalent bonds. Each molecule consists of two hydrogen and oxygen covalent bonds. However, when water molecules are placed together, as they are normally, the hydrogen atoms in each molecule can form hydrogen bonds with the oxygen atom of other molecules.
Hydrogen and oxygen atoms have different electronegativity values, which is the strength that they attract electrons with. This leads to dipole bonds where the hydrogen atoms are slightly positive, and the oxygen atom is slightly negative.
While a hydrogen bond may be called a bond by name, it is not an actual bond. However, it is a stronger interaction between hydrogen atoms and oxygen atoms of different molecules.