What is a pole in an error amplifier of an smps?

Hello,
Is it a specific frequency, or is it a trace on a bode plot?

In Marty brown book he shows an RC circuit and shows bode plots for it and says it is a "pole"..........but what is a pole? Is the pole the frequency at which the voltage transfer function through the RC circuit goes down by 6dB?....or is the RC circuit itself a pole?.....or is the pole just the gain and phase bode plots of this RC circuit?

In a type 2 error amplifier, there is a small cap (C1) used as feedback round the opamp, and this is in parallel with a series RC (R2, C2) circuit also used as feedback round the opamp.
Some books say that the pole of this network is 1/(2.pi.R2.C1)............ but that is a specific frequency, and a specific frequency isn't the same as the RC circuit shown in the Book by Brown.

So what is a pole?
One book says it is a system whose transfer function falls at 20dB/decade after the pole's 6dB point, and whose phase falls by 90 degrees around the 6dB point.

Another book says it is this...

1/[(1+(jw/(wp^2))]
where w = freq in rads/sec and wp = the pole frequency

Another says its the root in the transfer function.

Which explanation is right?

A pole is any value of s or w at which the denomenator of the transfer function becomes (or approaches) zero. When a system has a transfer function with just one dominant pole in it, it describes the cutoff frequency. But in systems with higher order transfer functions this is usually not the case.