Deadheading is the practice of removing flowers from plants when they are faded or dead. It helps to improve the appearance of most plants. More importantly, for many plants with extended flowering periods, deadheading helps encourage the formation of new flower buds.
It’s important to understand that deadheading is about more than just removing faded petals. The developing seed pod and, in most cases, the flower stem should be removed as well.
For more information about deadheading, see this useful post from the Royal Horticultural Society and this page from the Missouri Botanical Garden’s website (which is a treasure trove of valuable information for gardeners).