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The origins of this idiom.
The meaning of this phrase.
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Anything that requires minimal brain activity to accomplish. Usually said about decisions that are made, implying the decision was easily reached.
I'm about to state something completely obvious, so here goes: The decisions we make and the activities we do throughout the day require a brain. That's right! Even the simplest of tasks require some bit of brain activity to perform. Without a brain, well, we'd be dead and unable to do anything!

Still, despite this, there are menial tasks or easy decisions  that are sometimes considered to be 'no-brainers,' meaning a person shouldn't even have to use their brain to think when performing said tasks or making said decisions. For example, if someone is feeling generous and offered you a million dollars for absolutely nothing in return, many would consider the acceptance of that offer to be a 'no-brainer.'

There are other phrases with similar meaning to this one, which include 'it's not rocket science' and 'it's not brain surgery.' These three expressions all seem to have emerged pretty recently. This one in particular looks to only be around 60 or so years old. For example, the Lethbridge Herald newspaper from 1968 writes about an ice hockey coach, and he refers to the idiom:

"He'd break in on a goalie and the netminder would make one of those saves that our manager-
coach, Sid Abel, calls 'a no-brainer.'
* When presenting Charles with the choice of sitting inside all day doing nothing or going outside with me and having a little fun, well, it was a no-br
Note: The origins for most common idioms cannot be said with a certainty. What's provided are theories that may be plausible to how a phrase originated, but not necessarily so.

In addition, quotes that contain a phrase may be taken from old newspapers, poems, or books that were written centuries ago, but this by no means shows they originated from these. In all likelihood, if an expression is being used in a newspaper, it's probably already well known, and thus, from an older period of time.
ainer for him!
Know Your Phrase - The Meanings and Origins For Phrases and Common Idioms > N-Letter Sayings