There are many possible examples of situations in which supply or demand changes. We can see these operating in our economy all the time.
As an example of a change in demand, we can look at the demand for assault weapons. There are many on the political right who believe or at least fear that the government is going to ban assault weapons. In economic terms, they have experienced a change in their expectations about the future price (or, in this case, availability) of assault weapons. Therefore, they are willing to pay higher prices for such weapons today.
There are other examples in which supply changes. For example, the supply of electronic readers has gone up dramatically over the past few years. What this means is that companies like Amazon are more willing to make readers at a lower price. This comes about because it has become cheaper for these companies to produce the readers and the price of inputs/production is one of the major non-price determinants of supply.