We have genes called tumor suppressor genes, such as p53,  these genes make proteins that can repair damage to our DNA or they can kill cells on their way to becoming cancer cells. We have two copies of this gene, just as we have two copies of all genes. People who have a mutation in one copy of p53, meaning they only have one good copy, these people are prone to many different kinds of cancer. 

And elephants, what about elephants? Well they have 40 copies of p53!!!! No wonder they don’t get cancer!

http://blogs.discovermagazine.com/d-brief/2015/10/08/elephants-cancer-genes/#.VhnxjDf3bCR​