ELT is the usual short form of English Language Teaching: the work of teaching English to people who did not grow up with it as their first language. Teachers, training courses, journals, and job ads use it as the name of the field — methods, materials, classrooms, testing — not as a name for the English language itself. It sits beside TESOL and TEFL, which overlap a lot; ELT is the broader, often British-flavoured label for the profession. You will see ELT coursebook, ELT conference, a career in ELT. It is insider language: learners of English may never say it, but their teachers say it all the time. It is pronounced letter by letter, E-L-T. Though actually, those three letters can mean other things in other jobs; in a language-teaching context, this is the meaning that is meant.