Cas13a is a recent addition to the CRISPR-Cas toolkit that exclusively targets RNA, which makes it a promising tool for RNA detection. The protein uses a CRISPR RNA (crRNA) to target RNA sequences, which are cleaved by a composite active site formed by two 'Higher Eukaryotes and Prokaryotes Nucleotide' (HEPN) catalytic domains. In this system, an intriguing form of allosteric communication controls RNA cleavage activity, yet its molecular details are unknown. Here, multiple-microsecond molecular dynamics simulations are combined with graph theory and RNA cleavage assays to decipher this activation mechanism. We show that the binding of a target RNA acts as an allosteric effector of the spatially distant HEPN catalytic cleft, by amplifying the allosteric signals over the dynamical noise, that passes through the buried HEPN interface. Critical residues in this region - N378, R973, and R377 - rearrange their interactions upon target RNA binding, and alter allosteric signalling. Alanine mutation of these residues is experimentally shown to select target RNA over an extended complementary sequence beyond guide-target duplex, for RNA cleavage. Altogether, our findings offer a fundamental understanding of the Cas13a mechanism of action and pave new avenues for the development of more selective RNA-based cleavage and detection tools.