Meaning of zeros in transfer function
1)zeros with positive real part give a negative phase contribution, reducing the phase margin (which is bad) thus limits the performance of the system. 

2)Time delay in the system can also be approximated as a zero with positive real part (see first order Pade approximation 1), similar effect as previous point.

3)Blocking property of zeros, If you have a transfer function with a zero in the right hand plane, and an input tuned to that zero, then the output is at 0 for any time t. Example:

Proof for blocking property of zeros:3