Boob, booby trap, boobs

Jeremy the Boob, the foolish Nowhere Man in The Beatles' Yellow Submarine

You are probably aware that the word “boob” can be used to describe a “stupid”, “foolish”, or otherwise “clumsy” person. This particular definition is generally thought to have derived from the Spanish word “bobo” which roughly means “dunce.” This Spanish word comes from the Latin “balbus” meaning “stammering" and there is a theory that “boob”, meaning “stupid”, has Gaelic origins.

In English, this meaning appears in the late sixteenth century. later, it was applied to birds of the Sula genus that seem foolish because of their very large feet that make them rather clumsy walkers. They would often land on ships, were easy to catch and sailors began to call them “boobies.”

Much later, other things had the term attached with a similar meaning: the “boob-tube” for stupid TV programming, a “booby trap” being a trap that a foolish person would fall for, and a "booby prize” being a prize for the "top loser."

But somewhere along the way, "boobs" as a noun became slang for women's breasts. This usage seems to have gone wide around 1929 as U.S. slang, but the term boobies for breasts appears in the later 17th century. It may have been derived from the Latin puppa, literally "little girl," though it may also have come from the French poupe ("teat") or the German dialectal bubbi which begat the English bubby.

"Bubby" is defined as a vulgar slang that goes back to 1675 and it may have just evolved into "booby" then to be shortened to "boob." 

An explanation that is almost definitely not true, but is amusing, is that the word itself is a visual representation of what a pair of breasts.
Viewed from above B
Viewed from the front oo 

Viewed from a side view b

In 2013, an Australian women’s clothing chain, Bonds, found in a survey that 74% of Australian women typically used the word “boobs” to refer to their own breasts. The company decided to use the word in their “Bonds for Boobs” ad campaign to advertise their bras and as a partnership with the National Breast Cancer Foundation.