If the Nyquist plot passes through the critical point, s=-1+0j, then this means that the closed-loop poles, i.e. the zeros of the closed-loop characteristic equation, lie on the jw-axis. Hence, the system would be stable (bounded as t increases to infinity), but not asymptotically stable.
From a practical point-of-view, purely imaginary poles in the closed-loop system (as described above) are not usually desirable, in that this means the system will have oscillatory behavior. Thus, a well-designed closed-loop system should avoid such poles.