Why do people build their homes out of concrete? What are the advantages?

The answer comes down to any one of several points.

First, is it readily available as a building material? Throughout most of the world there are two favored building materials at the single home scale. Wood/timber and concrete/masonry. Basically, if wood is scarce or not suitable due humidity, mold, or infestation concrete or clay blocks, masonry, becomes the preferred method.

Second, strength or safety of the material. If you live where natural occurrences knockdown or destroy homes, like fires, occur regularly concrete or masonry construction tends to be more resistant, even without engineering. If, on the other hand, you are trying to build a large structure (spread out and/or tall), concrete is one of two options to obtain the strength and fire resistance you will likely need.

Last is aesthetics. Given that concrete is a very strong material when compared to wood while not being particularly confined to given shapes, it is a preferred material in architecture. It can be sculpted, shaped, textured, colored as one sees fit. You can also use smaller structural systems when compared to typical systems. (I do understand that concrete weight tremendously more than wood which results in thicker, more robust structural systems.)