"Anchor" just means a slow moving, far from perfectly accurate but (hopefully still useful) estimate of value of a currency. The authors start with a PPP estimate (left side), then try to modify it in an ad-hoc manner by using expected inflation differentials (right side of the equation), which presumably adjust more quickly (and are forward looking). So there is a slow component in the model (based on PPP, or purchasing power parity) (are you familiar with PPP?) and then another component based on expected inflation. PPI means producer price index and CPI means consumer price index.
Anchor is used in this way by FX economists. For example Rogoff (1996): "While few empirically literate economists take PPP seriously as a short-term proposition, most instinctively believe in some variant of purchasing power parity as an anchor for long-run real exchange rates.” Source: http://iei.liu.se/fek/frist/723G33/yinghong-files/1.463001/PPP_JEP.pdf an excellent article on PPP, by the way
It is a nautical analogy: although dropping an anchor will not fix the position of a ship (the ship will continue to be buffetted to and fro by winds and currents) it does guarantee that in the long run the ship will remain within a few hundred feet radius of where the anchor was dropped. So REER and PPP serve, at best, as some rough guide of where the currency will trade in the future, and other factors (the winds and currents) determine its day to day fluctuations.