Think of poles as time constants of a system's response. A single real pole corresponds to an exponential decay which you can observe, for example, in a heat transfer process.
A complex-conjugate pole pair represents oscillating behaviour - imagine a spring-mass-damper-system which can bounce. Its eigenfrequency is related to the pole pair's imaginary parts, while its damping / decaying characteristics is related to its real part.
Zeros are best imagined at the effect of anti-resonance. Say you shake a free spring-mass-system on one end (input) such that the other end stands (almost) still - then, the input signal you exert is eliminated through the system to the output (although inner variables are nonzero), and you see the effect of the system's zero. Things become interesting in multivariable systems (many inputs, many outputs) -- then you can distinguish into various types of zeros: invariant zeros and transmission zeros. For more details, refer to wikipedia or google these terms to find good lecture notes.
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