The local loop is the physical wiring that connects you to the public switched telephone network (PSTN). This line can be a voice line, or it can be a data line. The physical wiring for the local loop consists of a pair of twisted copper wires that run from the telephone company's central office (CO) to the subscriber's premise and another pair of twisted copper wires that run back to the telephone company's CO.
Your phone isn't directly connected to the local loop, though. Most homes today have a small gray box outside that is referred to as the Network Interface Device or "NID". The NID patches together the inside wiring and the outside local loop wiring. Together the two sets of wires create a duplex connection between the NID at the subscriber's premise and the CO over which an analog electrical signal is passed. Since this connection is local to the subscriber, it is called the local loop. Because this local connection spans the last few miles to the customer's location, it is also frequently called the last mile. In modern phone systems, the local loop runs from the last digital data point to the subscriber's premise and back.
The microphone in your telephone set (your phone) converts the sound of your voice into a series of electrical pulses that form an analog signal. The wiring inside your house carries that signal to the NID and passes it to the local loop wiring. The local loop then carries that analog electrical signal to the CO where other devices sample, quantize and encode the information in the analog signal, thereby converting it to digital data that will be time-division multiplexed over trunk lines (T1, T3, OC3, OC12, OC48, OC192 etc.).