A wingnut is a piece of hardware -- unsurprisingly, a type of nut. It is essentially a standard nut adorned with a pair of fixed 'wings' positioned to allow for easy turning with thumb and forefinger. They have many various uses, but are not very common in our everyday lives; they may perhaps be familiar to some from their frequent use in assembling drum kits.
Likewise, the wings are perhaps most familiar from the analogous wingbolt; while true wingbolts are also a rare find, the tuning pegs on most stringed instruments are similarly winged.
While wingnuts have the advantage of being easily tightened and loosened by hand, they have the disadvantage of being rather hard to tighten using a wrench, meaning that the average wingnut is probably a bit looser than the average nut. However, wrenches designed to fit over wingnuts are certainly available.
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Since the 1960s wingnut has also been used as a North American slang term to refer to a slightly crazy or loopy person. Whether this comes from the odd appearance, the weaker attachment to the relevant bolt, or just the sillier sound this adds to the traditional but harsher insult of 'nut' or 'nutcase', is anyone's guess.
In the 1990s wingnut became confabulated with the phrase "right wing nut", meaning someone who was both to the far right politically and nutty. Wingnut is now commonly used to refer to anyone you think is clearly very wrong and clearly too far to the right; the left wing counterpart is commonly said to be a 'moonbat'.