As a true child of the Google age, I can’t settle on not knowing the truth about this, so I took a break to do a search. Thefreedictionary.com gives the following two definitions:

1. (Linguistics / Letters of the Alphabet (Foreign)) the ninth letter in the Greek alphabet (?, ?), a vowel or semivowel, transliterated as i or j

2. (usually used with a negative) a very small amount; jot (esp in the phrase not one or an iota)

[via Latin from Greek, of Semitic origin; see jot]

This gave me no real explanation of where the word actually comes from, but it didn’t seem like there was some scientfic definition of just how little an iota is. Thus I had to keep searching.

It turns out, the expression actually has religious origins, as explained by the blog of Darren Greer (beware of horrible web design!):

During the theological debate that led up to the Council Of Nicea and the establishment of the Catholic church by Constantine in the 4th century A.D, one of the great debates was over the Greek word ‘homoousios.’ from the Aramaic bible. The question was whether that particular word was translated as stood or a single “iota” was added to make the word ‘homoiousios. The word, apparently, defined Christ’s relationship to The Holy Trinity and so was of real importance, though the difference between the words, in a phonetic and cursive sense, was almost negligible.

Wiktionary can further explain the importance of this:

From the difference between homoousios (“same substance”) and homoiousios (“similar substance”) in Christology, the names of those two competing viewpoints differing only by one ?.

This illuminates where the expression comes from. The difference of the single iota was actually very religiously significant. The use of homoousios rather than homoiousios established that Jesus actually was part of God, rather than being “more than human but less than God” which was the opinion of the Arianist faction of Christianity, not unlike what Islam thinks of him, by the way. The man named Arius was overruled by the council of Nicea and declared a heretic.

Of Arius, history tells that he later modified his teachings in order to be let back into Christian society, to the protests of his opponents. Just as he was about to be taken back he did however suddenly fall over and die, possibly poisoned by his opponents.

All over a single iota.