Rejection Sampling reasoning for Lattice Based Signatures
Narrow means that, with high probability, the ouput of the distribution is is small.
Small is meant in the sense of the Euclidean norm of a vector in the Euclidean space $\mathbb R^n$. More concretly, $v$ is informally said small to mean $\|v\| \leq B$ for some value $B &gt; 0$ chosen large enough for a given scheme to work out, but small enough for the lattice problem SIS to remain hard.
It is not a problem outside lattice based crypto because in a finite group $G$, if $x \in G$ is uniform, so is $x+c$. We can't simply do that over an unbounded space such as $\mathbb R^n$.