The coil is the indoor part of your AC
The indoor coil, a set of copper tubes and aluminum fins in the sheet-metal box on top of the furnace, does half the cooling work. Warm house air blows across it, the refrigerant inside picks up the heat, and two copper lines carry that heat outside.
Those two lines are the line set. The larger one is the suction line, wrapped in foam insulation. The thin bare one beside it is the liquid line.
Why the coil has to match
AHRI rates an outdoor unit and an indoor coil as a pair, and the efficiency on the label belongs to that pair. An old coil was built for a different unit and often a different refrigerant. Leaving it in place means you won't get the rated efficiency, and it can shorten the life of the new compressor.
Our AC prices include the coil. If a quote lists only the outdoor unit, ask which coil goes with it.
The line set might stay
A line set can be reused when it is the right size for the new equipment, holds pressure on a test, and can be cleaned. If it fails any of those, it gets replaced. Your quote should say which.
Drain and airflow
Cooling pulls water out of the air at the coil. That water runs down a drain line to a floor drain or a small pump, and the drain gets reconnected whenever the coil is swapped. While the coil is out, the installer should also check that the furnace blower can move enough air for the new system. ENERGY STAR lists airflow among the checks for a quality install.