Cisco is the leading maker of networking equipment. You may hear or read the word Cisco in several contexts.
First is as the company. Cisco makes the majority of routers and switches which are the equipment that connect computers and networks together. They used to mhave even a larger market share but it has declines. Cisco has been expanding in other areas related to networking including convergence (running computer, telephones and other devices on the same cable (which could be wire or wireless), security and conference calling among other areas.
Second is as a course. You may hear students say they are taking Cisco or others like me say we teach Cisco. In this case students are learning about computer networking and how to configure and maintain and connect Cisco routers and switches. Cisco has developed a complete curriculum called the Cisco Academy that is used by many schools to teach networking and Cisco equipment. Cisco trains the instructress and has reduced prices for equipment and has the complete courses.
Third is in terms of the equipment. You may hear people say they use Cisco equipment which is just the equipment built by Cisco and sold primarily under the Cisco name, but Cisco also owns Linksys which is the company they use to sale their products for consumers like your router or switch that are used in homes and small offices.
Fourth is as a certification. Cisco has a number of certifications for people in their technologies. Some common ones are CCENT, CCNA and CCNP. I am a Cisco Certified Academy Instructor (CCAI) meaning I am an approved experienced Cisco Academy instructor and I hold certification in field I am approved to teach in.