TEFL/TESL/TESOL are abbreviations for terms associated with the English language teaching industry (Teaching English to Speakers of Foreign/Second/Other Languages). All 3 terms refer to teaching English to students who do not speak English, or do not speak English as their native language.  Note: The US and UK define these terms with minor differences. 
 

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TEFL/TESL/TESOL Courses:  Refers to the courses people take in order to get TEFL certified.  

TEFL/TESL/TESOL Certification:   Refers to the type of certification people receive upon successful completion of a TEFL course.

TEFL/TESL/TESOL Certified:   Refers to people who are certified to teach English as a foreign/second language.
 

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TEFL (Teaching English as a Foreign Language):  Trains and prepares people, usually westerners from English speaking countries, to teach English in other countries where the primary language is not English.
Example:  A Brit goes and teaches English in Brazil

TESOL (Teaching English to Speakers of Other Languages): This term incorporates both TEFL and TESL and can generally refer to either one or both. 
Example:  An American teaching English to students who do not speak English as their first language in the USA or abroad.

TESL (Teaching English as a Second Language):  Trains and prepares people who want to teach English to non-native English speaking students in their home country.  
Example:  A native English speaking Canadian teaching English to a non-native English speaking Canadian in Canada (usually immigrants who want/need to learn English or foreign students)

CELTA (Certificate in Teaching English to Speakers of Other Languages): To the surprise of many, CELTA is not another broad term for describing the English teaching industry.  CELTA is actually a TESOL brand that was developed by, and operates under, the direction of Cambridge University.  Although there are lots of quality TESOL/TEFL brands in the world CELTA is generally viewed as the industry benchmark because of its standardized instruction and international reputation, however, there are many international TEFL and TESOL certification programs offering training, testing and support that exceeds CELTA.
 

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Broad Industry Terms

ELT (English Language Teaching) This encompasses the entire industry as a whole and is essentially what you will do as an English teacher. 

EFL (English as a Foreign Language) EFL generally refers to students who study English in non-English speaking countries.  For instance a Korean who studies English in Korea could be referred to as an EFL student.

ESL (English as a Second Language) ESL is typically a North American term associated with students who study English in an English speaking country such as the US or Canada.  It’s sometimes used as a broader reference to the English as a Second Language industry.