Regarding the Nyquist Criterion I recently read that with compressive Sensing it possible to sample the signal at a rate lesser than that suggested by Nyquist Criterion. However, I am still not getting how this is possible. Can someone suggest an intuitive way of understanding this concept of sampling at lower rates? And if this is possible, do modern communication techniques use this concept?
The Nyquist criteria refers not to the frequency, but to the bandwidth, which is related to information density in a signal.  A very high frequency signal, of approximately known frequency, with a sufficiently small bandwidth, will still be aliased or folded down with baseband frequencies by undersampling.  But if the bandwidth (or other known characteristics) of the signal is known to rule out other aliased frequencies (such as the non-existence of baseband spectrum content), that knowledge in conjunction with the undersampled samples may still provide enough information to reconstruct the signal.