Why do entertainment system headphones on aircraft have two pins?
The three main reasons are:

Prevent theft of headphones due to incompatibility with home systems
Redundancy, if one connector breaks, the other will still provide audio
Before the 3.5mm jack was used, a pneumatic system was in use, which required two connectors.

This question has been asked on different websites already, but here is a detailed explanation that sums it up nicely:

There are a couple main reasons:
First, the airlines were trying to prevent theft of headphones. The two-pronged plugs have been around on airplanes since way before the airlines started charging for headsets. Back then, headphones were not usually easily carried around as the portable earbud style had not become popular yet. By using a two-pronged setup that is not used in most other audio systems, the motivation for passengers to steal the headsets went down immensely.
The second reason is redundancy. When a standard stereo headphone jack with three internal connections (right, left, and ground) breaks, you will often lose audio in both the left and right channels. However, with the two-pronged design, if one of the jacks breaks then there will still be audio going through the other channel. While this is annoying for the user, it is an easy way for the airline to defer maintenance on that individual seat's audio system until both the left and right channel are non-functional.
The two-prong design is a relic of the past, before headphones were bundled with so many of the mobile devices we now buy. Planes with updated inflight entertainment (IFE) systems usually have the standard stereo jack as most passengers prefer using their own headsets now. Slowly these old connectors will be completely phased out.
Another less obvious (and probably less likely, but interesting nonetheless) reason, though, is based on airline complacency. Airlines, especially US based airlines, are notoriously slow in changing their tactics. Back before the 3.5mm jack became the standard for headphone audio connections for IFEs, airplanes used a pneumatic headphone design. These headphones were similar to stethoscopes where hollow tubes would be plugged into the armrest which had actual soundwaves coming out (instead of analog electrical signals). These systems were much more reliable than the standard electrical system and the headsets themselves were very cheap to replace. Since the pneumatic system required two separate plugs for the left and right channel (since you cannot mix physical sound waves into a single hole), all armrests were designed with two holes for audio. Airlines were likely so used to having two jacks for audio that they continued with the same design when they switched to electrical audio signals.
(Source: www.quora.com - Author: Raj Misra)