Backdoor Trojan
In short: A backdoor trojan opens a back door for attackers to remotely access the infected system.
In more detail: After infection the program connects to a server of the attackers or waits for incoming commands. This lets the attacker copy files, start programs, use the webcam or load further malware.
In Depth
Remote access trojans (RAT)
Well-known examples in the past: Back Orifice and SubSeven. Today there are many RATs, some of which also abuse legitimate remote maintenance functions.
Detection
Unusual outgoing connections, unknown autostart entries, high load without a visible reason. A firewall with rules for outgoing traffic helps.
Related
Backdoors in general, remote control, botnets.
See also: Trojans, Backdoors, Remote Control (by Attackers)