Google Play services is a set of background services that runs on all Google-certified Android devices, together with a family of SDKs (software development kits, code libraries for building apps) that use those services. Google updates it automatically, separately from updates of the operating system, the phone maker and the carrier.
An app includes only a lightweight client library for each SDK it needs, declared as a dependency in the app's Gradle build file. At runtime the library talks to the full implementation inside the Google Play services app on the device; this saves storage and memory and delivers bug fixes without an app update. SDKs cover Google Maps, Google Pay, Google Sign-In, Firebase Cloud Messaging, location, ML Kit, AdMob and more. An app should check that the service is present with isGooglePlayServicesAvailable(), because devices without the Google Play Store do not have it. Support starts at Android 7.0 (API level 24).
Google distributes the SDKs through its Maven repository; the pages read state no price.