A target registration point (TRP) is a special location on the battlefield which has been "pre-registered" for an artillery strike. The TRP's exact location and distance is known to both the spotter and the firing element, allowing the gun to place fire there with almost no time spent once they receive the orders to fire.
Note that in real life, target registration was performed by a battery of guns in contact with an observer; thus, a real life "TRP" would be particular to a particular battery. Combat Mission abstracts this so that TRPs apply to all artillery on the side, except for on-board artillery which has moved after setup.
Placement of TRPs during setup is not limited to friendly zones; a TRP may be placed on any action spot on the map. Once setup is over, TRPs are immovable. TRPs are also secret: the enemy cannot spot them in any way.
Artillery strikes targeted within 50m of a TRP do not require line of sight from the spotter, do not use or need spotting rounds, and have a near-zero preparation time. (The "communication" time is unaffected, so don’t expect battleships or corps-level rockets to be on hair-trigger readiness due to a TRP.) TRPs do not affect the dispersion (accuracy) of artillery fire; the pattern of shells is unaffected.
In Combat Mission, TRPs double-function as "ambush" placements for regular fire. When any unit fires any weapons at a target near a friendly TRP, it will be much better at estimating the range correctly.