What is ESD? Electrostatic Discharge! That little spark you sometimes get when you touch a light switch or some other grounded object. Electrostatic discharge is always an issue when working with electronic equipment, but is a particular problem during the winter months due to dry indoor air. When low temperature outside air enters a building and is heated the relative humidity drops considerably. Dry air conditions increase static charge buildup.
Why should you care? Well, if you are working with APM and build a large static charge on your person, then transfer that charge to APM (which may (or may not) be signaled by your touching it being accompanied by a spark), that may cause damage to the autopilot. The hardware multiplexor on APM is particularly susceptible to damage from ESD, but many other components can be damaged as well.
How can you avoid damage from ESD? There are a variety of products and techniques that can help. Best practices would include using an anti-static mat on your work surface and using a wrist strap to ground your body to the mat when working on APM. However, simpler, lower cost things can help a lot. Pay attention to what clothes you are wearing when working on APM. You may want to remove your fleece jacket or wool sweater. When I sit down to work with APM I try to momentarily ground myself when first sitting down at my bench to drain any accumulated charge I am carrying, and do so every time I leave and come back to the bench. Also, there are a variety of household anti-static products that can be very effective in lowering the amount of static charge you pick up. I use an aerosol anti-static product that will treat a room with a few seconds spray, and which will last several days.
Like they say - "An ounce of prevention...."