A base station (or basestation) is a wireless transceiver at a fixed location (e.g. atop a telephone pole) which is part of a wireless communications network, e.g. the cell phone network. Typically, the base station connects to any cell phones in its area and relays the calls to the wired network.
A femto base station is a smaller, personal base station which might cover a home or building and connect via a DSL Internet connection.