What does it mean?
This is a generic diagnostic trouble code (DTC) for the powertrain and generally applies to OBD-II equipped vehicles with cruise control. This may include, but is not limited to, vehicles from Peugeot, Ford, Nissan, Chevrolet, Hyundai, VW, Audi, Citroen, etc. Although generic, the exact repair steps may vary depending on the year, make, model, and powertrain configuration.
In the vehicle’s cruise control option, there are many functions. The operator can not only set a specific speed for the vehicle, which can be automatically maintained using many sensors, switches, modules, among many other components, but you can also change the speed electronically (i.e., “set -” & “resume +”), temporarily change the speed while remembering the previous speed (e.g., overtaking vehicles, unexpected stopping/slowing down), among others.
Since most of the functions mentioned in the description of P056A and related codes (P0565, P0566, P0567, P0568, P0570, etc.) are contained within a switch/component, it should be fairly straightforward to locate the input mechanisms (buttons, switches, conversations, etc.) involved. That said, some common names for said components are: Multifunction Switch, Steering Wheel Controls, Cruise Control Switch, Cruise Control Module, Accessory Switch, etc.
What happened, in the case of this code, is that the ECM (Engine Control Module) detected one or more malfunctions in the signal circuit. In other words, something went wrong in the circuit of the function mentioned in the description.
When the ECM detects a signal malfunction in one or more of the many cruise control functions, it illuminates the CEL (Check Engine Light) with P056A and/or related codes. Most likely, the use of this function will be disabled and/or will behave abnormally.
The P056A code is set when the ECM detects a malfunction in the INCREASE DISTANCE signal of the adaptive cruise control (ACC) system.
NOTE: ACC systems are not only complex in their design but also require special tools and/or diagnostic procedures to properly correct any present faults.
An example of cruise control buttons on a steering wheel:

How severe is this DTC?
The severity would be considered moderately low. Even if you lose all cruise control functionality, you can still operate safely. Regarding additional damage if left unaddressed, this would be the rare case where you might be able to neglect it if, say, your vehicle is old and you can live without cruise control, or you cannot afford to repair the vehicle.
That said, it is possible that neglecting ANY electrical issue long enough could lead to additional damage.
What are some of the symptoms of the code?
Symptoms of a P056A trouble code may include:
The cruise control indicator light on the dashboard does not illuminate or is steady
Inoperative cruise control
Unable to set the cruise control to the desired speed or the speed is irregular
Certain functions within the cruise control system are non-operational (e.g., Resume, Set, +, -, Coast, Accelerate)
Controls do not work consistently
What are some common causes of the code?
Causes
of this P056A code may include:
Faulty and/or damaged cruise control switch or buttons inside the switch
Connector(s) not making a proper and effective electrical connection
Wire(s) in the cruise control harness have been stripped and/or damaged, causing a short circuit, open circuit, resistance, etc.
Cruise control switch assembly contaminated by liquid (coffee, soda, juice, etc.)
ECM problem
Faulty cruise control module
BCM (Body Control Module) problem
Overheated parts causing malfunction
What are the troubleshooting steps for P056A?
Basic Step #1
The first thing I would do here is visually inspect the cruise control switch/module. Sometimes buttons are missing, soda has jammed the button in one position, buttons are loose and not making the proper electrical connections. That said, ensure that the buttons controlling the cruise functions move freely and are not contaminated by potentially damaging particles and/or dirt. You will also want to record ALL malfunctions or anomalies of the cruise functions.
Basic Step #2
Does the cruise control indicator light illuminate in the instrument cluster when the cruise control is manually activated? If not, you may want to check if there is a fuse for the circuit. This information should be found in the make and model’s service manual. Replace any blown fuses with new, manufacturer-approved fuses.
Basic Step #3
To access the cruise control switch/module harness, as a rule, you will need to remove some dashboard parts (e.g., steering column cover, airbag module in the steering wheel, etc.). To locate the specific wire involved in the fault, you will certainly need the appropriate wiring diagram for your vehicle. These vary considerably for many reasons. Always obtain the proper service information BEFORE performing anything too invasive.
Basic Step #4
It’s a good idea to ensure that your ABS (anti-lock braking system) is in good working order and that no ABS warning light is illuminated on the dashboard. The ABS uses many sensors, including speed sensors which, if malfunctioning, could trick the computers into thinking the vehicle is traveling faster or slower than the actual speed.