What are poles and zeros?
Take the equation b/(x-c) with b non-zero.  The ratio goes to infinity as x approaches c.  So c is the location of a pole (something tall and pointy in a graph).

Take the equation (x-b)/c with c non-zero.  The ratio goes to zero as x gets closer to b.  So b is the location of something commonly called "a zero".

You can not only do this with scalar x, but with complex x, thus the domain of the poles and zeros will be on a (complex) plane instead of on a line.

If the ratio represents something about the response of a filter, it might say the filters output is at or near zero when the input is at or near a response "zero".  And bad things might start to happen when x gets close to a pole (power supply starts smoking when asked to supply infinite amps, math operations produce NaNs or fixed-point overflows, etc.)