Rayon-core represents the "core, stable" APIs of Rayon: join, scope, and so forth, as well as the ability to create custom thread-pools with ThreadPool.
Maybe worth mentioning: users are not necessarily intended to directly access rayon-core; all its APIs are mirror in the rayon crate. To that end, the examples in the docs use rayon::join and so forth rather than rayon_core::join.
rayon-core aims to never, or almost never, have a breaking change to its API, because each revision of rayon-core also houses the global thread-pool (and hence if you have two simultaneous versions of rayon-core, you have two thread-pools).
Please see Rayon Docs for details about using Rayon.
Rayon-core currently requires rustc 1.28.0 or greater.