Don't pay too much
Also used in terms of a trade in. Many parts say at your auto store require a CORE to exchange for a rebuilt carburetor, alternator, starter or water pump. Same with an engine. Most of the time you don't get the core back, you receive another unit rebuilt. For aircraft engines it is basically a usable engine that can be rebuilt. There is an expectation that major parts of the engine can be reconditioned and reused.
Keep in mind if you by an engine as a core for trade in for a rebuilt they will charge you for any parts that are not servicable or usable. A bad crank, case or cam could ruin you budget. Items usually rebuilt or refurbished are the case halves, rods, crankshaft, cam, lifters, gears and many times cylinder to name a few. Items like nuts, bolts, pistons, rings, bearings, valves and guides are replaced with new. Lycoming has a service letter describing a complete list of parts that should be replaced in an overhaul.
Most important do NOT pay to much for a core, even if it has 100% serviceable parts. A rebuild can easily cost up wards of $9,000-$12,000, more if any major component is not usable. A replacement of the crank for example is roughly $4,000. If you pay too much for a core and have to replace any major component, you might as well have bought a new engine for appox $20,000. It would be cheaper. Most cores are going for about $3,000-$6,000. Sometimes they are sold as running engines with usable time left. If the engine is sitting on the floor in the corner of a hanger it's hard to know if it's usable. Last advice. If the "CORE" does not come with excellent records, log books, the core is not worth much. You have to verify what kind of condition the engine is in. If it is not currently in a plane and running that is hard to do. This is where good records are so important. BUYER BEWARE! Most companies want TOO much for their JUNK. Usually the best cores come from a senerio like another RV builder is upgrading to a larger engine and sells their existing engine.