Definition
The user element of a GPS system is the GPS receiver and antenna installed in the aircraft (or carried by the pilot), which receives signals from the GPS satellites, processes them, and computes the aircraft's position, altitude, ground speed, and time. It is one of the three segments of the GPS system, alongside the space element (the satellites) and the control element (the ground monitoring and control stations).
Plain English
It's the GPS unit in your aircraft -- the box and antenna that pick up the satellite signals and turn them into your position on the moving map.
Context Anchor
Seen in discussions of GPS components, along with the satellite and ground-control parts of the system.
Derivation
Called the 'user' element because it is the part of the system operated by the end user -- the pilot. The satellites and ground stations exist to support it, but the user element is where the navigation actually happens for the person flying.
Why Pilots Care
The user element is the only part of the GPS system the pilot directly interacts with or has any control over. Its capabilities, database currency, and approvals determine what kinds of navigation and approaches the aircraft is legally and practically able to fly.
Intuition Check
Do not read user element as only the pilot. In this context, it mainly means the GPS receiving equipment used by the pilot or aircraft.
Example Sentence 1
The user element in our aircraft is a panel-mounted GPS receiver with an externally mounted antenna on top of the fuselage.
Example Sentence 2
Loss of signal at the user element can interrupt GPS navigation during an instrument approach.