ESL is an acronym for English as a Second Language.
ESL students are people learning English as a second language, that is, as another language after their mother tongue or primary language.
Teachers who teach ESL classes are defined as TESL teachers as they Teach English as a Second Language, which is different from teaching English as a native language. To become a TESL teacher you need specific teacher qualifications.
Compare ESL to EFL which is English as a Foreign Language. This is taught to students who are living in a non-English speaking country and wish to learn English for business or pleasure, etc.