What is so special about this filter coef = [1,2,1]?
It is a symmetric odd-sized FIR smoothing kernel, belonging to the class of Pascal or binomial filters that somehow sample a Gaussian kernel. Plus, its coefficients are simple dyadic integers, that can be implemented as bit-shifts 1/4 1/2 1/4. The coefficients sum to one, hence it is unit gain at DC.

In simpler word: (one of) the simplest real smoother preserving symmetric feature location. It's efficiency is however limited