The term "wireless" refers, in the most basic and obvious sense, to communications sent without wires or cables. It is a broad term that encompasses all sorts of wireless technologies and devices, including cellular communications, networking between computers with wireless adapters, and wireless computer accessories. Wireless communications travel over the air via electromagnetic waves (radio frequencies, infrared, satellite, etc).
"Wireless" on its own is typically used to refer to products and services from the cellular telecommunications industry; CTIA, "the Wireless Association", for example, is composed of wireless carriers, cell phone manufacturers, and others in the mobile phone market. Different cellular protocols and standards include CDMA, GSM, EV-DO, 3G, and 4G. The term "wireless Internet" will most often be referring to cellular data, though the phrase can also refer to data access via satellite.
Networking technologies that connect multiple computers and devices together without wires -- i.e., in a wireless local area network or WLAN -- also fall under the wireless umbrella. Often, instead of referring to just "wireless" for these technologies, the term "wi-fi" or "wifi" will be used. Wi-fi covers technologies that incorporate 802.11 standards, such as 802.11g network cards and wireless routers.
More: Find out more about the differences between cellular wireless data and using wi-fi for Internet-on-the-go