  We present an explanation for the well-known observation that complexity of
the solar magnetic field is a necessary ingredient for strong activity such as
large eruptive flares. Our model starts with the standard picture for the
energy build up -- highly-sheared, newly-emerged magnetic field near the
photospheric neutral line held down by overlying unsheared field. Previously,
we proposed the key new idea that magnetic reconnection between the unsheared
field and neighboring flux systems decreases the amount of overlying field and,
thereby, allows the low-lying sheared flux to ``break out'' (Antiochos, DeVore
and Klimchuk 1998, ApJ, submitted). In this paper we show that a bipolar active
region does not have the necessary complexity for this process to occur, but a
delta sunspot has the right topology for magnetic breakout. We discuss the
implications of these results for observations from SOHO and TRACE.
