DNA changes naturally with time, we can see this through the evolution of all living things. The process by which this happens is essentially a series of mistakes. When DNA replicates (makes a copy of itself), which it has to do every time a cell divides, there is a 1 in 3 billion chance that it will make a small mistake somewhere. Even when DNA is not doing anything, it can sometimes just spontaneously change, and this happens more frequently under certain conditions like UV light or with radioactive waves (or a radioactive spider bite). These changes in the DNA are called ‘mutations’. The word itself implies a negative effect, but actually most mutations are totally harmless due to the many safety systems the cell has to deal with them. In addition, some mutations are beneficial, and it is in these cases that you get natural selection and evolution. A famous example of this is what Charles Darwin saw in the Galapagos, finches (a kind of bird) from different islands had different beak shapes, which matches with what kind of insects or food was available in each habitat.
Scientists have been aware of how important mutations in the DNA are for a long time. Cancers, for example, result from an accumulation of mutations in a few cells, which give them an advantage over their neighbours, and make them grow out of control. Many researchers are interested in how we can change this process. Can we actually make mutations in exactly the way we want for our benefit? ‘Genetic modification’ or GM has completely transformed the field of biology and enabled the development of a huge number of drugs. The thing is, all we're doing is copying what happens in nature.