For public computers, your browser history, the websites that you have visited, can be accessed by everyone who uses the same computer. The information you have filled out on a form maybe automatically saved by the browser. If someone goes to that same form or another one, they may be able to view your information when the browser tries to automatically complete(auto complete) each field on the form based on information that was previously entered by you or other users.
Also, these public computers may be infected with keylogger programs, which will record your every keystroke and send it to criminals. The keystrokes sent back can be your credit card number that you have entered on a shopping cart check-out page. Some of these malicious programs may also have screen capture that will take pictures of your screen and send it to criminals.
To be on the safe side when shopping online this holiday season, please use your home, office, data providers' internet connection, or if you are going to use public Wi-Fi, use a trusted VPN provider.