Here Hartshorne's definition of a closed subscheme of a variety which is local complete intersection:
Now suppose that $D$ is an effective divisor (Weil or Cartier) on $X$. My question is the following:
1) What is the meaning to say "$D$ is local complete intersection"? I suppose that one wants to say that " the support of $D$ is local complete intersection".
2) Once that the previous point is clarified I'd like to know under which conditions on $D$ we can conclude that it is local complete intersection.