I remember having to manage so many folders of mp3s, manually syncing them to devices. And paying $.99 a song meant a very limited selection. I often relied on free iTunes playlists to find new music, because I couldn't afford to buy new music at the time.
They've eliminated all of these problems. Pay $10-15 a month, and you can listen to whatever you want, wherever and whenever.
I say this purely from the consumer's perspective, though - I'm not super familiar with what artists' experience is like. On one hand I'm sure Spotify broadens your audience quite a bit, but I wouldn't be surprised if artists run into issues similar to creators on other platforms (e.g. YouTube).