Cancer is caused by DNA damage.
A cancer is swarm of identical, rogue cells, which copy themselves over and over again, taking up more and more space, and using more and more resources (Oxygen, energy, space, etc.). A benign tumor's cells eventually stops replicating. A malignant tumor (a cancer) never stops.
Right, so DNA...
As you know, DNA is a cell's issue of instructions for copying itself, so having damaged DNA is like having a scratched CD, the data is corrupted. And if you put that CD in a burner and made copies, you'd get copies of that corrupt data. Fun, eh ?
So here's the interesting part. Your cells have built-in regulations to prevent the progression of "corrupted data". Your cells scan themselves continually and if they find their DNA to be damaged they self-destruct through "apoptosis".
("Apoptosis" is also how your body handles the flu', so that's possibly one reason why you feel weak. It's a good idea to eat lots of protein when you're sick so you'd have materials to make new, replacement cells.)
Your cells also have a fixed number of times which they are allowed to [replicate, determined by the length of their chromosomes' [URL="http://en.wikipedia.org/wiki/Telomere"]telomeres](http://en.wikipedia.org/wiki/Mitosis).
Each time one of your cells replicates, its telomeres shorten a little. When telomeres get too short, the cell no longer can copy itself, and instead ages until it dies.
However, damage to the correct part of a cell's DNA, can induce the cell's internal regulations to switch off. A cell whose telomeres never shorten, for example, will be able to go on replicating indefinitely. And it does. And that mass of cells is what makes up cancerous growths.
So what causes DNA damage ?
Here's where I finally answer your question.
DNA can be "damaged" by internal mutations, genetic errors passed on through generations.
Or through exposure to chemical "carcinogens", substances which for various reasons promote cancer. Smoke, rancid oils, etc.
OR though radiation. Radiation is a stream of sub-atomic particles emitted by a source. These sub-atomic particles can slam into cells and physically damage them... or physically damage their DNA . "Scratching the CD," so to speak. And, as I said above, if the right part of the DNA is damaged, the cell may lose its internal regulation.
So you can see there why a healthy person, who doesn't smoke, who doesn't eat carcinogenic foods, can still possibly develop cancer, if (in this example) he is exposed to too much strong radiation, to the point that some of his body's cells experience the right kind of DNA damage.
That's one possibility. I'm sure there are others out there and we'll discover more in future.