In a covalent bond, electrons are shared between two atoms. For example, in H2, each hydrogen atom donates an electron to form a single bond consisting of two electrons. These two electrons reside in a molecular orbital (as opposed to an atomic orbital) which lies in between the two hydrogen atoms.
In dipole-dipole interactions, there is no sharing of electrons. The interaction is an electrostatic interaction (i.e. an attraction between a positive and negative charges). It is similar to the attraction between Na+ and Cl- in the ionic bonds of table salt, but dipole-dipole interactions are much weaker because molecules with dipoles do not carry full positive or negative charges. For example, in acetone (which has a dipole), the oxygen carries a slight negative charge while the carbonyl carbon carries a slight positive charge.
In water, some electrons are shared between the lone pair of the oxygen in the hydrogen-bond acceptor and the hydrogen in the hydrogen-bond donor. So instead of being just a weak electrostatic interaction between the slight positive charge of the hydrogen and the slight negative charge of the oxygen, the bond is said to have characteristics of a covalent bond because of the sharing of electrons. Since covalent bonds are very strong, this slight covalent character greatly strengthens the interaction between water molecules.