What is ECI?

External Call Interface 

ECI calls are the way of communication between CICS and Web Services which uses TCP IP connections.

Client Side or Web Service need not use BMI setups to connect to CICS online transactions.

ECI calls are set up and linked the CICS default transaction. And on the client side or Web Service side can be set up in a way where it can run on mirror transactions

Read Blog for more reference  : TCPIP CONNECTION BETWEEN CICS AND WEB SERVICES