Up to this point I know that two equal and opposite electric charge constitute an electric dipole. But when I study the "Introduction to electrodynamics" by DJ Griffiths, the author a consider a single charge as an electric dipole which is at a distant $$d$$ from the origin. Now in what sense a single electric charge can be considered an electric dipole and What is correct definition of electric dipole?
Dipole moment $$p$$ is defined to be $$p=\sum_{i} q_i\vec{r_i}$$ where $$q_i$$ is the charge, and $$r_i$$ are the charge and position vector measured of the ith particle measured from the origin. So dipole moment is a perfectly well-defined quantity even if there is only one charge. If you happen to choose the origin of your coordinate to be where the one charge is, then the system has zero dipole moment. Otherwise, it has nonzero dipole moment.