I assume it's an ideal that generates the whole Ring.
Also is $(x+y)^2$ a non cyclic ideal of $R=\mathbb{C}[x,y]/(x^2,xy,y^2)$.
The notes I'm using don't give a definition of a cyclic ideal, assume it's the same as definition of cyclic group but with group replaced with ring.
Found the definition, now. An ideal M is cyclic if $M=\{rm: r \in R \}$ for $m \in M$.