A tumour is simply a space-occupying lesion (something that should not be there, that is; a "lump") caused by abnormal cell replication.
(In medicine, the word "tumour" literally means "swelling", and can sometimes refer to that instead, but that's a different story).
Cancer is a disease in which cell replication is totally out of control. What causes cancer is damage to the genes (DNA) which normally stop cell replication when it needs to be stopped.
There's no such thing as an "ordinary tumour"; all tumours are abnormal. However, what makes a benign (harmless) tumour different from a cancerous tumour is that there is still some mechanisms stopping the cells inside the tumour from replicating; they are doing it more than they should, but they are not totally out of control. When those last mechanisms are broken too, the tumour is cancerous.
(This is a simplified explanation; the actual explanation is a semester-long university course. It's mostly accurate for the layman, though)