An MA in EFL/TESOL will enable you to get a job teaching English as a foreign language at university level. That seems obvious, so I'm not sure what else you wanted to know. Obviously, there are far more jobs overseas than in the UK or USA, but you could teach on pre-sessionals in the UK. That said, many universities are looking for an MA in TESOL plus some experience of teaching EAP. Pre-sessionals are not permanent positions - just two months in the summer.
If you're looking for something full-time or permanent, you would have a better chance in Asia or the Middle East than in Europe, although many universities ask for 3 publications and/or a PhD. That said, an MA alone would probably get you work in less desirable/lucrative locations. Much of the work is part-time. You will almost certainly not get a full-time teaching post in the UK or USA without a PhD.
If it's commercial EFL schools you're looking at, you should not need an MA, but a post-graduate diploma in TESOL would be helpful to get a better-paid or more secure job.
If you want to work in a high school overseas, a PGCE or equivalent teaching license would be more useful than an MA.
I hope this helps.