KnowYourPhrase.com - The Meanings and History For Popular Idioms and Phrases
Sheds are most often located somewhere in a person's backyard, and are used to store belongings. A common thing to find in sheds are tools of various kinds, some being sharp, others dull. Speaking of those two words: The word sharp has been used to describe someone who is keen, or clever. The word dull, on the other hand, has been used for the opposite—to describe a person who is slow, or unintelligent. Thus, when it's said that someone is 'not the sharpest tool' it is being implied that the person is stupid.

This phrase looks to be a very recent one. The earliest I could find this expression in writing, for example, is from the Colorado Springs Gazette Telegraph, July 1994, where it reads:

    "Critics said that Cliburn was an intuitive artist, and that once his intuition was exhausted, he had little 
     else to say about a piece — which was a fancy way of saying that Cliburn wasn't the sharpest tool in 
     the shed."
* When it comes to cooking, I'm not exactly the sharpest tool in the shed, so I keep my meals basic most of the time. They still taste good, though!

* My orange cat is not the sharpest tool in the shed, but that's okay, he's still adorable!
Note: The origins for many popular expressions are unclear. In these cases, what may be provided instead is a theory as to how a phrase may have originated. If no theory is given, then I'll try to at least include a quote on the page to give you an idea for how old a phrase is. So, for example, if there's a quote from an old poem from the year 1650, that does not necessarily mean the expression originates from the poem or year, it simply means the saying is at least that old.

N-Letter Sayings  |  Know Your Phrase - The Meanings and Origins For Phrases and Common Idioms
N-Letter Sayings
Meaning:
Origins:
Example Sentences:
Phrases and Idioms
A hand tool called a saw. Be careful, it's sharp!
Someone who is thought to be unintelligent; stupid.