Use the > About This Mac to determine what version of OS X you're running, and which model of Mac is in use.
Available updates are distributed by > Software Update, and upgrades can be purchased from Apple, or sometimes on the used market.
All eMac systems are using PPC processors and not Intel processors, and are all incapable of running the current OS X software, nor any version past 10.5.8. Subsequent versions are Intel-only.
You can likely still purchase a PPC 10.5 distribution used (or possibly by calling Apple directly?), though that upgrade — if you're not already running 10.5 — won't get you a version new enough for the recent/current versions of iTunes.