The term "base station" was first used to refer to the towers you see on the side of the road that relay cell phone calls. These stations handle all cellular calls made within their area, receiving information from one end of the call and transmitting it to the other.
In the computer world, however, a base station refers to the wireless access point for computers with wireless cards. It is basically a router that communicates with devices based on the Wi-Fi standard. Some common Wi-Fi configurations include 802.11b and 802.11g. Wireless base stations are made by companies such as Netgear, Linksys, D-Link, Apple Computer, and other manufacturers. Fortunately, as long as the hardware is based on the Wi-Fi standard, all wireless cards can communicate with base stations from any manufacturer.