The iCloud Music Library is an online collection of music that's fed by two services: iTunes Match and Apple Music.
iTunes Match is like an online music locker; it scans your iTunes collection and gives you access to any tracks it already has on its servers. Additionally, it uploads any songs it can't find and lets you access or download them with all your registered devices. It costs $24.99 a year. Apple Music includes a very similar service alongside its streaming options, but with one key difference. Its "scan and match" feature includes DRM, so even though you can download them they will cease to function if you cancel your subscription. It costs $9.99 per month for an individual membership, $14.99 per month for a family.
Apple's 25,000-song limit was making its music locker services a tough sell. A couple of services were beating or getting close to that figure free of charge: Google Play Music lets even non-paying subscribers store 50,000, while Microsoft's Groove Music lets you play any track in your OneDrive for free. Amazon only offers 250 tracks for free, but for the same $24.99 per year as iTunes Match you get storage for 250,000 tracks.