Jaccard index is the ratio of the size of the intersect of the set and the size of the union of the set.
Jaccard distance $d_J(A,B)$ is defined as
If the two sets are the same, $A=B$, we have $J(A,B)=1$ or $d_J(A,B)=0$. We have maximum similarity.
If the two sets have nothing in common, we have $J(A,B)=0$ or $d_J(A,B)=1$. We have minimum similarity.