Three circles which are linked together - BUT - no two circles are attached to one another.
The name "Borromean rings" comes from their use in the coat of arms of the aristocratic Borromeo family in Italy. The link itself is much older and has appeared in the form of the valknut on Norse image stones dating back to the 7th century.(Image and text from Wiki, via Kottke)
The Borromean rings have been used in different contexts to indicate strength in unity, e.g. in religion or art. In particular, some have used the design to symbolize the Trinity. The psychoanalyst Jacques Lacan famously found inspiration in the Borromean rings as a model for his topology of human subjectivity, with each ring representing a fundamental Lacanian component of reality (the "real", the "imaginary", and the "symbolic").
The Borromean rings were also the logo of Ballantine beer.