What is TEFL / TESOL?

TEFL stands for Teaching English as a Foreign Language.
TESOL stands for Teaching English to Speakers of Other Languages.
Both are used to represent teaching certifications accepted around the world.
TEFL and TESOL are basically the same thing. The only difference is that TEFL is the term widely used in the UK and TESOL is more common in USA, Canada and Australia.

Common acronyms are

ESL - English as a Second Language
ESOL - English to Speakers of Other Languages
EFL - English as a Foreign Language
ELT - English Language Teaching
TESL - Teaching English as a Second Language