All this has been around for a long time. What your students are going to do is to remove a small portion of a carrot's root and make those cells multiply into a non-differentiated mass. I am going to define cancer in some very narrow terms. Cancer is simply the massive multiplication of 'normal' somatic cells. Cancer in humans are not inheritantly bad cells, they are just rather mixed up.
Cancer kills by getting in the way of normal bodily processes.
I prefer to keep it rather simple for the kids. Plant cancer is similiar. I will define it as 'massive cellular growth without cellular differentiation'. Plant cancer is most often seen as 'galls' on trees. You may know that this gall formation is caused by a bacterium, Agrobacterium tumafecians .