External Short Messaging Entity (ESME) is a term originally coined to describe an external application that connects to an SMSC to engage in the sending and/or receiving of SMS.
Typical examples of *ESME*s are systems that send automated marketing messages to mobile users, voting systems that process SMS votes etc.
Anytime a mobile user sends/receives a message to or from a party that is not a real mobile user, you can be fairly sure that the other party is an ESME.