You can use iTunes to host your own recordings - for example ripped from your own CDs. This costs nothing.
You can purchase songs or albums from the massive library in the iTunes Store - the cost varies. One purchased they are yours to keep and load onto an iPod. This has been the case since the Store was introduced. More recently the facility was introduced to download purchased songs onto another device - 'iTunes in the Cloud'.
'iTunes Match' makes all items in your iTunes collection available online for access to your other devices. Songs you have purchased will be available, as with 'Tunes in the Cloud'; songs you have for example ripped from CDs you have bought will be matched by the version in the Store if this is available; if it isn't available your copy will be uploaded for access by other devices. It costs $24.99 per year. If you stop the subscription you can still play anything you've downloaded, though you cannot upload or download any more songs.
You can subscribe to the newer Apple Music service, which allows you to stream or download for offline listening a large proportion of the songs in the library. The cost is $9.99 per month. This gives you access to a vast number of songs, but obviously if you terminate the subscription you can no longer play the songs. Downloaded songs can only be played on the device which downloaded them, and therefore cannot be loaded onto any other iPod than the Touch.
This page gives a lot more detail: http://wilmut.uk/applemusic