That is a function word used in the English language for several grammatical purposes.
These include:
In the first two uses the word is usually pronounced weakly, as /ðət/, whereas in the other uses it is pronounced /ðæt/.
In the Old English language that was spelled þæt. It was also abbreviated as a letter Thorn, þ, with the ascender crossed, ꝥ ( ). In Middle English, the letter Ash, æ, was replaced with the letter a, so that that was spelled þat, or sometimes þet. The ascender of the þ was reduced (making it similar to the Old English letter Wynn, ƿ), which necessitated writing a small t above the letter to abbreviate the word that ( ). In later Middle English and Early Modern English the þ evolved into a y shape, so that the word was spelled yat (although the spelling with a th replacing the þ was starting to become more popular) and the abbreviation for that was a y with a small t above it ( ). This abbreviation can still be seen in reprints of the 1611 edition of the King James Version of the Bible in places such as 2 Corinthians 13:7.