What's its use of the nonsingular 2-step nilpotent Lie algebras which form an a class of 2-step nilpotent Lie algebras ?
Recall: A $2$-step nilpotent Lie algebra $N$ is non-singular if $ad X : N \to Z$ is surjective for all $X\in N-Z$. Where $Z$ denote the center of $N$. Here $ad X (Y) = [X,Y] \, $ for all $X,Y\in N$.
Example: The Heisenberg algebra is nonsingular.
Tank you in advance
Nonsingular $2$-step nilpotent Lie algebras are of special importance in geometry. P. Eberlein, one of experts here, says it as follows: "Nonsingular and almost nonsingular Lie algebras are the most well behaved of all 2-step nilpotent Lie algebras". I think you should read one of his papers on Geometry of $2$-step nilpotent Lie algebras, to convince yourself of the "use".