"As you type into the search box, Google Suggest guesses what you're typing and offers suggestions in real time. This is similar to Google's "Did you mean?" feature that offers alternative spellings for your query after you search, except that it works in real time. For example, if you type "bass," Google Suggest might offer a list of refinements that include "bass fishing" or "bass guitar." Similarly, if you type in only part of a word, like "progr," Google Suggest might offer you refinements like "programming," "programming languages," "progesterone," or "progressive." You can choose one by scrolling up or down the list with the arrow keys or mouse."
The technology is powered by some pretty smart algorithms which use a wide range of information to predict the queries you are likely to enter; it does not base its suggestions on your personal search history.