My understanding is that one big thing that differentiates cancers from benign tumors is that cancers tend to break apart and spread to other parts of the body. The amount and speed with which this happens varies with the type of cancer. If you catch them early, certain types of cancer have a decent chance that they haven't broken up and spread yet, so there can be a reasonable chance of cure by surgically removing the primary tumor.
But other cancer types may spread like wildfire. If you go in to surgically remove them, you may find dozens of secondary tumors throughout all tissues in the body. It simply isn't feasible to remove them all; if you don't get every last one, chances are good that whatever's left will grow and spread again, damaging any tissues that are invaded. Additionally, chances are very high in this case that there are many more microscopic tumors or bunches of cells that would never be found surgically. In that case, chemotherapy (cancer killing chemicals injected into the bloodstream) or radiation are the primary options, but only if the type of cancer responds well to those treatments.
I'm not a doctor, so anyone feel free to correct any of the above.
As an example, I had a type of cancer called seminoma. It doesn't grow as quickly or spread as readily as many other cancers, so surgery can often be curative when caught early. I had the surgery, but 6 months later a new tumor showed up in one of my abdominal lymph nodes. That means a microscopic clump of cancer cells was left behind after the surgery, and eventually migrated to the lymph node where it attached and grew. We didn't know this until the lump became large enough to be observed on a CT scan.
Since there were likely to be other microscopic bits of cancer floating around besides this one, we did radiation in that area of the body to get them all. Seminoma spreads in a slow, stepwise fashion, going first to the abdominal lymph nodes, then later the lungs, and finally maybe the brain. Because it doesn't do this quickly, we a had very statistically high chance that radiation to the abdomen only would get everything. If that weren't the case, and there were a significant chance of cancer cells existing outside the abdomen, then chemo would have been the only real option. It would have gotten everything since it goes throughout the entire body via the bloodstream.
Hope that helps.