The whole "RNP APCH" thing is something new as of mid-2018, called the PBN Box. Performance Based Navigation. Eventually, you'll start seeing that on most all RNAV procedures. You'll also start seeing more specific RNAV requirements. Along with PBN for RNAV approaches, a similar box is being added in the same location of traditional ground-based approaches listing required equipments. It gets confusing when you have multiple chart notes in multiple places that specify things like "ADF Required", etc. The intent of the new boxes is to simplify equipment requirement notes and consolidate them to one standard location.
The confusion seems to come from the choice of letters, RNP. RNP, or Required Navigational Performance, is nothing more than a spec of how precise the GPS is. Where the confusion comes is in the naming - currently, the FAA names "general" RNAV procedures "RNAV (GPS) Rwy xx". Those are procedures that bug-smashers like us in the 91 world can fly. "RNAV (RNP) Rwy xx" procedures are limited to operators who have specific authorization to use them, generally via an OpSpec or LOA. We call them RNP-AR approaches - authorization required. They require fancier hardware and training. A lot of those procedures will contain things like RF, or Radius-to-Fix legs, and other fun elements that a majority of GA GPS units cannot fly. The GTNs do have the ability to fly RF legs after a certain software update, but I don't believe there are any non-AR approaches with RF in the US NAS. Bottom line - you shouldn't ever see a procedure in your GPS that you won't be able to fly. Just know the line(s) of minima that you can use, and choose your DA/MDA based on that. Non-WAAS limits you to LNAV minima, while WAAS opens up LP and LPV. In some cases, the LPV minima will be as low as 200', which match most standard Cat I ILS minima.
Almost all applicable RNAV procedures that have been amended since, I believe, AIRAC 1806, have had this added. It doesn't mean too much to the average 91 pilot, as long as you have a suitable approach-capable GPS unit. The link posted earlier helps explain it. A non-WAAS 430/530 will still allow you to fly the approaches, but only to the LNAV MDA minima. Newer units like the 430W (W being the abbreviation for WAAS) and the GTN series will allow you to fly down to the lowest minima published as long as GPS integrity is maintained. If the unit loses the required number of satellites during the approach, it will display some sort of RAIM loss annunciation and/or display LNAV annunciations, depending on the unit.
