What does EID mean on my iPhone 15?

With an American iphone 15 you have two EIDs in Settings, General, About, one for each eSIM. The numbers will be unique to your phone. Some providers use EID to manage your cellular provision. Apple don't generally use EIDs, prefer to use serial number.

Hard to say without any context.

It can be anything from a Muslim holiday to an identification number for an esim (Embedded Identity Document).

Where are you seeing this "EID"?