In astronomical interferometry, the correlator is the device or software that interferes the waves to produce the interference pattern.
At visual wavelengths, interference is typically done optically, but at longer wavelengths, the signal can be digitized to the point where digital signal processing in hardware or software can do the work. It may be done in real time, or for very-long-baseline interferometry, it may be done by bringing the signal data (necessarily including precise timing) together as digital files later.
For any direction other than exactly vertical, the waves reach the antennas at different points in time, the antenna further from the source receiving each wave crest last, the period of time being termed a geometric delay. The same delay can be imposed on the signal from the nearer antenna, and the correlator can amplify those signals (voltage level) received by both by multiplying the two. The rise and fall of the resulting signals as the Earth turns (due to the received signal being centered on the antenna and slightly off) offers the most precise data regarding position in the sky, i.e., is what yields the extremely high angular resolution: angular distances are derived from the time periods over which the changes occur.