What does having complex conjugate zeros implies?
I know that if I had two complex conjugate poles in the system, this
  implies having some damping in the frequency response, but what does
  having complex conjugate zeros implies?


Possibly a simple way of looking at this is to imagine that you have a low pass filter with a damping ratio (\$\zeta\$) less than 1 (complex poles) and you used it in a negative feedback branch of a regular amplifier you will get zeros replacing the poles.



Assume that K = \$\dfrac{\omega_n^2}{s^2+2\zeta\omega_n s + \omega_n^2}\$

After it is used in the feedback loop you get: -

$$H(s) = \dfrac{s^2+2\zeta\omega_n s + \omega_n^2}{s^2+2\zeta\omega_n s + 2\omega_n^2}$$.

Notice the \$2\omega_n^2\$ in the denominator (in case you missed it) and also notice that you have conjugate zeros in the numerator.