First of all, a single water molecule consists of an oxygen atom attached to two hydrogen atoms. Each of the hydrogen atom is bound to the oxygen atom through a covalent bond. Why the bond is covalent can be explained by looking at the electronegativities of each atom.
A covalent bond is a type of bond where the atoms involved share electrons in order to obtain an octet (8 electrons). Oxygen has 6 electrons, and by sharing electrons with 2 hydrogen atoms (each sharing one electron), it attains an octet. The hydrogens only need two electrons (exception to octet). This is as opposed to an ionic bond such as in NaCl where one of the atoms completely transfers the electron to the other. Covalency is greatest when the two atoms have almost equal electronegativities. Electronegativity is the measure of the tendency of an atom in a bond to attract the shared electrons towards itself. Hence, the atom with the greater electronegativity will attract the electrons more towards itself (this results to polar bonds). If the electronegativity between the two atoms is very large, the bond formed is more likely to be ionic. As a rule of thumb, if the difference in electronegativity is less than 0.4, the bond is considered non-polar; between 0.4 and 1.7, the bond is polar. Both of these are covalent bonds. Above 1.7, the bond would be considered ionic.
In the case of water, the electronegativity of oxygen is 3.5, while that of hydrogen is 2.1. The difference is 1.4, and hence the bond is a polar covalent bond with electrons tending to be closer to oxygen since it is more electronegative. In summary, water has a covalent bond because of the nature of oxygen and hydrogen -- they share electrons to attain stability, and their electronegativities are close enough for their bond to be considered covalent.
A covalent bond usually describes a bond between nonmetal elements. You can look on the periodic table that clearly labels the differences between non-metals, transition metals, alkaline metals, and metalloids and image any compound that is only made of non-metals will be covalent. H2 is a diatomic gas and O is also gas both are non-metals. So by default water has a covalent bond.
The definition of a covalent bond is a chemical bond shares electron pairs between two or more atoms. The charges of these atoms do not add up to become 0, unlike ionic bonds.
Water is composed of two hydrogen atoms and an oxygen atoms. Covalent bonds' strong characteristic lies in the difference of electronegativity in the atoms. Any Delta electronegativity below 1.7 in a molecule shows that the bonds in the molecule is covalent. Hydrogen's electronegativity is 2.2, and oxygen's is 3.44. The Delta electronegtativity is 1.24, and 1.24 is less than 1.7, thus the bond is covalent.