Essentially TEFL is teaching English to people who need the language for business or for pleasure or for an exam. In most cases TEFL students will be living in their own (non-English speaking) country and will use English only to converse with foreigners. At work or with their family they will most likely use their own mother tongue.
Contrast this with TESOL (Teaching English to Speakers of Other Languages) and TESL (Teaching English as a Second Language) which are teaching students who are learning English because they are living in an English speaking country (such as the UK or the USA) and where they need English for everyday use outside the home.
Note that to teach TEFL you normally need to take a TEFL course.Image © Renato Ganoza