iTunes Match is a subscription service from Apple that allows the user to access their music library anywhere, even if they do not have the song files downloaded locally on their computer/device. Apple Match was released with iTunes 10.5.1 on November 14th, 2011.
iTunes Match is meant to allow people to access their library of already-owned songs across their devices without requiring the local storage needed to do so. It is separate from Apple Music in that you must own the songs first before being able to listen to them, as Apple Music allows you to listen to any songs regardless of whether or not you own them (aka a music streaming subscription).
iTunes Match allows you to upload up to 100,000 songs from your library, and it will play the stream the song when you play it on a device that is connected to the internet. The music from iTunes Match is DRM free, unlike Apple Music. iTunes match "matches" music from your library with one already on Apple's iTunes Store and plays that version when you stream it. If no match is found, it will instead stream the user's uploaded music file. "Matched" songs will stream at the standard iTunes 256kb AAC file, even if your original music file was of lower, higher or lossless quality.
The current cost of iTunes match is $24.99 USD per year. (same as when it was released 2011).
Apple Support's Page on iTunes Match: https://support.apple.com/en-us/HT204146
iMore.com article about iTunes Match: https://www.imore.com/itunes-match
Macworld.com article on the release of iTunes Match: https://www.macworld.com/article/1163219/apple_releases_itunes_10_5_1_with_itunes_match.html