The answer is in the Private Pilot ‒ Airplane Airman Certification Standards
Task B. Airworthiness Requirements References 14 CFR parts 39, 43, 91; FAA-H-8083-2, FAA-H-8083-25
You should read and understand CFR §91.203, §91.205, §91.207, §91.209, §91.213, and §91.215.
The DPE will want to know that the aircraft is legally permitted to operate in the airspace that you will be taking your practical test in.
They will check that the AR(R)OW documents are in the aircraft—Airworthiness Certificate, Current Registration, probably not Radio License since it is not likely your test will take you to another country, Operating Limitations, and current Weight and Balance. Operating Limitations would include placards; any documents required by STCs for installed equipment e.g. GPS or autopilot; and for newer aircraft flight manual (AFM) for that aircraft.
They will check the logbooks to make sure that the aircraft is legal maintenance-wise. Annual Inspection and 100-hour AD items obviously. Some 100 hour items can be signed off by the pilot e.g. Bendix switch check while others need to be signed off by an A&P e.g. muffler shroud inspection. Most A&Ps use a computer system that prints out a list of ADs and when they were complied with. It is a good idea to put a sticky-note on the annual and recurring ADs pages so you don’t waste time looking for them.
ELTs are checked at annual time, but battery replacement can get out of sync with the annual and they will check that. If you are taking the test in an aircraft with an electrical system, the transponder must be working and checked in the last 24 months. You don’t need a pitot-static check for a private checkride, but if you are going to file and fly IFR flight plan—as you will for your instrument rating you will need one.
If there is any inoperative equipment e.g. LORAN then it must be logged and marked.
ADSB isn’t required yet, but after January 1, 2020 if you fly in the covered areas your aircraft must have it installed. CFR §91.225.
On an instrument check-ride the DPE will want to see that the database is current if you have a GPS and that the VOR check has been done.
They will also check to make sure that your medical is current and that you have all of the endorsements necessary for the aircraft e.g. complex, high performance, tailwheel.