The photon goes through one (or both) of the two slits, whose paths are shown as red or light blue lines, indicating which slit the photon came through.
So far, the experiment is like a conventional two-slit experiment. However, after the slits a beta barium borate crystal (labeled as BBO) causes spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical entangled photons with 1/2 the frequency of the original photon. These photons are caused to diverge and follow two paths by the Glan-Thompson Prism.
One of these photons, referred to as the "signal" photon (look at the red and light-blue lines going upwards from the Glan-Thompson prism), continues to the target detector called D0. The positions where these "signal" photons detected by D0 occur can later be examined to discover if collectively those positions form an interference pattern.
The other entangled photon, referred to as the "idler" photon (look at the red and light-blue lines going downwards from the Glan-Thompson prism), is deflected by a prism that sends it along divergent paths depending on whether it came from slit A or slit B.
Somewhat beyond the path split, beam splitters (green blocks) are encountered that each have a 50% chance of allowing the idler to pass through and a 50% chance of causing it to be reflected. The gray blocks in the diagram are mirrors.
Because of the way the beam splitters are arranged, the idler can be detected by detectors labeled D1, D2, D3 and D4. Note that:
If it is recorded at detector D3, then it can only have come from slit B.
If it is recorded at detector D4 it can only have come from slit A.
If the idler is detected at detector D1 or D2, it might have come from either slit (A or B).
Thus, which detector receives the idler photon either reveals information, or specifically does not reveal information, about the path of the signal photon with which it is entangled.
If the idler is detected at either D1 or D2, the which-path information has been "erased", so there is no way of knowing whether it (and its entangled signal photon) came from slit A or slit B.
Whereas, if the idler is detected at D3 or D4, it is known that it (and its entangled signal photon) came from slit A or slit B, respectively.
By using a coincidence counter, the experimenters were able to isolate the entangled signal from the overwhelming photo-noise of the laboratory - recording only events where both signal and idler photons were detected.
When the experimenters looked only at the signal photons whose entangled idlers were detected at D1 or D2, they found an interference pattern.
However, when they looked at the signal photons whose entangled idlers were detected at D3 or similarly at D4, they found no interference.