Classification- A data-set can have different groups/ classes. red, green and black. Classification will try to find rules that divides them in different classes.
Custering- if a data-set is not having any class and you want to put them in some class/grouping, you do clustering. The purple circles above.
If classification rules are not good, you will have mis-classification in testing or ur rules are not correct enough.
if clustering is not good, you will have lot of outliers ie. data points not able to fall in any cluster.