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A leased line is a telephone line that has been leased for private use. In some contexts, it's called a dedicated line. A leased line is usually contrasted with a switched line or dial-up line.
Typically, large companies rent leased lines from the telephone message carriers (such as AT&T) to interconnect different geographic locations in their company. The alternative is to buy and maintain their own private lines or, increasingly perhaps, to use the public switched lines with secure message protocols. (This is called tunneling.)