What is meant by the break frequency of an op-amp?
The open loop voltage gain of a opamp decreases proportional to frequency.  Or, you can say if falls of at 20 dB/decade.  At some point this gain becomes 1.  This is characterized by the gain-bandwidth product spec.  For example, a opamp with 1 MHz gain bandwidth product has a gain of 1 at 1 MHz, a gain of 10 at 100 kHz, 100 at 10 kHz, etc.

For most applications, this simple formula is enough.  However, note that this indicates infinite gain at DC.  Opamps do have very high gain, like 100k or 1M or more at DC, but not infinite.  Starting at the unity gain frequency, the gain goes up by 20 db/decade (10x voltage gain per decade) of lower frequency, but only until it hits a certain point.  That point is the break frequency.  Lower frequency doesn't result in much higher gain anymore.

For example, consider a opamp that has a 5 MHz gain-bandwidth product and 1 M (120 dB) DC voltage gain.  It's break frequency is therefore 5 Hz.  That's the point at which you get the DC voltage gain by following the gain-bandwidth formula.  Whether you get there by dividing 5 MHz by the 1 M voltage gain, or go 6 decades of frequency down to make up the 120 dB, you get to the same answer.

Another way to look at this is that a opamp can be modeled as a large DC gain (1 M in the example above) with a low pass filter at the break frequency.

For most circuits, the break frequency by itself is of little interest.  Opamps are therefore usually specified to have a minimum gain-bandwidth product and a minimum DC gain.  Also note that these specs are minimums.  You can't really rely on the break frequency being in a particular place.  Both the actual gain-bandwidth and actual DC gain could be higher, each implying a different break frequency.