The word semiconductor comes from semi (meaning half) and conductor. It refers to a material that has some, but not all, of the properties of an electrical conductor.
A semiconductor is somewhere between being an excellent conductor such as copper, and an excellent insulator such as glass or plastic. Therefore, it will sometimes conduct electricity, depending on electrical stimulation in a specific direction. As a result, it is a good material to be used as an electronic switch, either conducting or not conducting, thereby providing the 1s or 0s required in binary computing and digital processing-based systems.
Semiconductors are important because they can be constructed to conduct electricity better than other materials, a fact which makes them perfect for many applications.