To shorten something by cutting off the top or the end. The editor decided to truncate the article to fit the space available in the magazine.
To reduce the number of digits in a decimal number by dropping some of the least significant digits. The software will truncate the number to two decimal places for simplicity.
In computing, to shorten or clear (a file, database table, or log) to a specified length, often zero. The system automatically truncates the log file every 24 hours.