A remote attacker could have exploited a variety of issues related to web browser security, including cross-site scripting attacks, denial of service attacks, and arbitrary code execution.
For a more detailed description of the security problems, you can visit Canonical's security notification.
Users can simply fix the security flaws by upgrading the operating systems to the latest libwebkitgtk package, specific to each distribution.
A normal system update, executed with the Update Manager, will implement all the necessary changes. A complete system restart is not necessary.