Tavis Ormandy discovered a format string vulnerability in ImageMagick’s file name handling. Specially crafted file names could cause a program using ImageMagick to crash, or possibly even cause execution of arbitrary code.
Since ImageMagick can be used in custom printing systems, this also might lead to privilege escalation (execute code with the printer spooler’s privileges). However, Ubuntu’s standard printing system does not use ImageMagick, thus there is no risk of privilege escalation in a standard installation.
ImageMagick is also commonly used by web frontends; if these accept image uploads with arbitrary file names, this could also lead to remote privilege escalation.