What is the role of pyrophosphatase in RNA polymerization?
This question can be answered by considerations of chemical equilibrium. For any chemical reaction:
$$\ce{A + B &lt;=&gt; C + D}$$
It is a property of nature that removal of product ($C$ or $D$) from the reaction mixture drives the reaction in the forward direction. This is an example of le Chatelier's principle and can be explained as follows:
In a reaction mixture containing $A$, $B$, $C$ and $D$, the rate of forward reaction ($A + B \rightarrow C + D$) depends on the frequency of collision of $A$ and $B$ molecules. Similarly, the rate of backward reaction ($C + D \rightarrow A + B$) depends on the rate of collision of $C$ and $D$ molecules. The collision frequencies, in turn, increase with concentration of the relevant species. An abrupt reduction in the concentration of $C$ hinders the backward reaction while leaving the forward reaction unchanged. Thus the forward reaction begins to dominate.
The reaction catalysed by RNA polymerase is:
$$\ce{RNA + NTP &lt;=&gt; Longer \ RNA + PP_i}$$
By removing $\text{PP}_i$ from the reaction mixture, pyrophosphatase does exactly that and drives the reaction in favour of RNA polymerisation. Note that hydrolysis of pyrophosphate is favoured because of the negative free energy change associated with it (thanks to David for pointing that out).