EID stands for eSIM Identifier (sometimes Embedded Identity Document). It's a unique 32-digit number burnt into every eSIM chip at manufacture, similar to how every phone has an IMEI.
How to find your EID
Dial *#06# on most phones — the EID appears alongside your IMEI. On iPhone: Settings → General → About. On Android: Settings → About phone → SIM status.
Why it matters
Carriers use your EID to provision an eSIM profile specifically to your device. If you change phones, the EID changes, and you'll need to re-provision your eSIM on the new device.