This is the basic principle of supply and demand and is at the heart of any market-based economy. Essentially, you must look at supply as the quantity that is available of a given product. Demand refers to the relative number of people who want that product. The greater the demand, the harder it is for the supply to meet that demand. Producers can only create a certain amount of any one product in a given amount of time and with a sometimes limited set of resources needed to create that product. As a result, quantities (supplies) are limited, making them more valuable and, consequently, making people who can afford to pay more willing to pay more. Sometimes, even people who cannot afford to pay are willing to pay the price if the demand is great enough. Conversely, when the supply ourweighs the demand, you end uo with a surplus. The suppliers have created a product that consumers are not purchasing rapidly enough. In this case, proces will be dropped in order to encourage people to buy the product and reduce the supply.

For a look at some relevant graphs explaining the process, see the following resource:

This is for the same reason that increased demand leads to higher prices in microeconomics.

The idea is that there is greater demand, which means that there are more people who are willing to buy a given product.  When that happens, the people are typically willing to pay higher prices because they know that if they do not pay that price, someone else will and the product will be gone.

So when there is more demand, there is more "money chasing goods" and the prices have to rise and you end up with demand-pull inflation.