Predictive text input or Predictive Text Entry, (also know by the most popular type, T9,) allows you to enter text by pressing only one key per letter on a keypad where multiple letters share keys. As you enter a word, the phone will automatically compare all of the possible letter combinations against a built-in dictionary of words, and determine which word you intended to type. If it guesses incorrectly, you can scroll through other possible words without re-typing the word.
This makes it much easier to enter long text messages and e-mail. The number of keystrokes is typically cut in half when using predictive text entry, compared to traditional methods, which require you to press 2 once for A, twice for B, three times for C, and so on for each key on the keypad.
Predictive text is most useful on 12-key and 20-key phone keypads, but it can be used on QWERTY text keyboards as well.
There are a handful of competing technologies, including T9 from Nuance, Motorola's iTAP, and eZiText from ZiCorp (now owned by Nuance.) T9 is the most popular. iTAP is used by Motorola in some (but not all) of its own phones.