If you synchronised the music from "iTunes" - that is, your iTunes Library, on your computer, then the music should still be listed in your Library now. That's probably what someone meant by "being accessible from iTunes".
However, if for some reason, you don't have access to that Library:
- if any music on your iPod was purchased directly from the iTunes Store using your iPod, then use iTunes (on your computer) to sign into your account and you should be able to download the music again from there
- for any music purchased from other sources (such as Amazon), go to your account with that store and look for your past purchases, so that you can download them again
Once you recover or re-build your Library, might I suggest that you make sure to back up your music in the future?
- an iPod is not a back up for what is on your computer. It's the other way round, the music stored on your computer is the back up for the iPod
- but computer hard drives can fail, so back up the music on the computer as well. Buy yourself an external hard drive to use as back up for your computer