The open loop frequency response is the frequency response of the amplifier with no feedback, or before feedback, or with the feedback network delibirately broken.
The closed loop frequency response is the frequency response of the amplifier with feedback.
These two are closely related. The theoretical closed loop frequency response is equal to the open loop frequency response times the amount the feedback. If you have 40 dB (100 times) of feedback, and an open loop response of 1 kHZ, the closed loop frequency response is 100 kHz.
The formula relating these two are:
where D is the feedback factor and Aol is the open loop gain. The total denominator expression is what we call feedback.
The open loop ferquency response is determined by the internal compensation (intended or not) of the amplifier. Many amplifiers are designed with one stage having a very high output impedance, thus the spreading capacitance of that stage's output, determines the open loop frequency response. For integrated circuits the open loop frequency response is either specified or you can see it graphically as a function of gain. In the latter case, look at the maximum gain, which means zero feedback.
Just to remind you, the closed loop gain Acl is related to the open loop gain, Aol, in exactly the same way as the frequency response, althought inverse.
At Electrocompaniet the thinking was in favour of a large open loop bandwidth. This is also my opinion, but I feel it shall not be larger than necessarry. There is always a tradeoff, and if you go for too high an open loop bandwidth, you reduce the possible amount of feedback you can have. My thinking is that as long as the open-loop bandwidth is high enough, you should use the rest of your gain for feedback. This will give you a more optimal design, because the overall distortion will be reduced.
What determines the open loop bandwidth
Mostly it is determined by the last voltage amplification stage. The collectors of this stage (assuming transistor amplifiers, which these articles are all about :-)) is connected to the bases of the drivers of the output stage. The input impedance of these drivers are normally very nonlinear, and strongly frequency dependent. This means you can very well get a major pole here which varies strongly with signal level and the load (loudspeaker and cables) of the output stage. The solution to this is to voltage drive the output stage, thus loading down the amplification stage. This will also have the effect of pushing up the cut-off frequency at this point. The EC amplifiers have this pole around 500 kHz. The benefits of a voltage driven output stage is described elsewhere on this site, among them an AES paper, links will arrive.