An Exit is the means through which Redpills leave the Matrix to return their consciousness to their body lying in their hovercraft. Operatives must find and use the proper object that allows their mind's communication with the Matrix to be safely disconnected. This can only be achieved with a land line telephone.
History
In The Matrix Trilogy, the differences between cell phones and wired telephones were never discussed, but viewers are led to understand in the first minutes of The Matrix that a "land line" phone is needed to leave the Matrix. Trinity (secretly deceived by Cypher) is found by Agents, but cannot retreat from Room 303 of the Heart O' The City Hotel because the Agents "cut the hard line." Trinity eventually escaped by using a telephone booth.
Later, Agents again attempt to trap the Nebuchadnezzar crew by cutting the hard line in the Lafayette Hotel and then changing some elements of the hotel to eliminate a conventional means of escape.
A plausible reason why cell phones cannot be used to exit the Matrix involves a real-world technology used to prevent cell phone calls from being intercepted; encryption of the call so that only the caller and the answerer can hear the content of the call. It is possible that an exit must be on an unencrypted line, unlike a cell phone.
Another plausible reason to require a hard line phone is that conventional telephones within the Matrix are wired into the infrastructure of the city (and, logically, the main communication algorithms of the Matrix proper). It appears (based on the scene in The Matrix where the Neb crew enters the Matrix on their ill-fated mission to the Oracle) that operators prefer, or find it easier, to hack operatives into the Matrix through the Matrix's telephone system programming. In the scene, the operatives appear near the phone as they materialize within a room.
Entering the Matrix through one hard line does not required to exit with the same hard line. Link hacks an entrance for Trinity and her motorcycle several stories above ground atop a parking garage during her mission to ensure that Neo's mission to the Source would succeed after the crew of the Vigilant are killed (The Matrix Reloaded). Neo himself would show that his powers as The One enabled his mind to enter Mobil Avenue station without a phone or the use of an operator or hovercraft.
Appearances
A typical rotary telephone used as an exit.
The majority of the exits used by redpills are rotary dial telephones either connected to a hard line within a building or in a phone booth. Redpills generally try to exit the Matrix in private areas where they can pass undetected by bluepills or agents.