The words jot (iota, Strong's Concordance #G2503) and tittle (keraia, Strong's #G2762) appear only once in the Bible. Jesus' statement using jot and tittle occurs near the beginning of his famous Sermon on the Mount likely given from Mt. Eremos.
Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled (Matthew 5:17 - 18, KJV).
What are they?
Jot is the English translation of the Greek iota, which itself was derived from the Hebrew letter yod (yodh). Both the letters iota and yod are the smallest of their respective alphabets.
Iota, from the fourth century B.C. forward, was the ninth letter of the classical Greek alphabet. When it was used to symbolize a number, however, it represented 10 (Universal History of Numbers, section on Greek alphabetical numerals). Yod is the tenth of twenty-two Hebrew letters and represents the number 10.
Tittle, which comes from keraia, means "a little horn," "horn like" or an apex or point. It can refer to a diacritical dot placed over abbreviated words and some letters. It can also reference the apex or point of certain Hebrew letters called a tag (taga). A tag is a small decorative "crown" placed on letters to distinguish them from others in the alphabet. Sometimes more than one crown or tittle is drawn (1906 Jewish Encyclopedia on Tagin).
Why are they used?
Jesus, before launching into the main teaching section of his Sermon on the Mount, makes it plain that he did not come to do away with (abolish) God's commandments or to the remove the requirement to keep them. He came, rather, to be a perfect example of how to live life based on every word that proceeds from God (Matthew 4:4).
Don't suppose (most Christians do the exact opposite!) that I came to do away with the Law and the Prophets. I DID NOT COME TO DO AWAY WITH THEM, but to give them their full (spiritual) meaning. Heaven and earth may disappear. But I promise you that not even a period (jot) or comma (tittle) will ever disappear from the Law . . . (Matthew 5:17 - 18, CEV).
The Lord used a jot and tittle, the smallest letters and marks, to underscore his life and teachings should NOT be interpreted as annulling God's law. The necessity of learning and obeying the commandments continued during his life, was required of the New Testament church, and continues today into the future (see Revelation 12:17, 14:12). Those who refuse to keep the commandments will not be in God's Kingdom (22:14 - 15)!
Did you know . . .
If a scribe, making a copy of God's law, was found to have omitted a tag (tittle) from a particular page his entire work would be destroyed (People's Dictionary of the Bible).
Surprisingly, English has several idioms related to jot and tittle. The phrase "not one iota" is used to relate that not a single tiny bit of something will be used. Another phrase is "dot the i's and cross the t's." It is used to delineate taking care of every detail or being completely thorough (e.g. the creation of terms in a legal contract).
The phrase "to a T" is used to describe something that is perfect, exact or complete (e.g. the clothes a person wears fits them in every detail). The likely source for using the letter T in this idiom is the word tittle (World Wide Words).