Material culture and nonmaterial culture are both expressions of a society. The former refers to the physical and tangible expressions of that society and the latter involves its values and ideas. Anthropologists and sociologists study both nonmaterial and material culture to get a fuller understanding of a society.
Material culture exists in the form of buildings, household and religious objects, and public spaces. Think of the objects and buildings that you would expect to see in just about every neighborhood in your society. If you are in North America, you could expect to see schools, houses of worship, homes of a certain size and style, parks and playgrounds, and roads. Inside most homes, you would expect to see a television or two, framed photos, wardrobes, furniture, and more. These are all expressions of culture in a material form. Traveling around the world and moving from culture to culture, you would see great variation in this. For instance, homes in Japan tend to be smaller and traditionally lack the furniture you're likely used to. Instead, people traditionally sit on rice fiber mats called tatami laid out on the floor.
Nonmaterial culture refers to intangible expressions of culture. In other words, it is the beliefs, values, language, norms, morals, and actions that help to define a particular society. In North America, for instance, it is common for people to shake hands when they meet. In most of East Asia, people bow. Even this action varies in form throughout the region. In much of Europe and Latin America, people greet each other with a kiss (or several kisses, depending on where you are) on the cheek. These are not material objects, but expressions of nonmaterial cultural norms.