My understanding is that it's meant to be an enterprise tool for Sys admins of business and schools to allow for remote monitoring and troubleshooting, but because it's expensive to make two sets of devices, it's in everything.

Relevant bits from that wiki:

The Intel Management Engine always runs as long as the motherboard is receiving power, even when the computer is turned off.

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Intel's main competitor AMD has incorporated the equivalent AMD Secure Technology (formally called Platform Security Processor) in virtually all of its post-2013 CPUs.

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Critics like the Electronic Frontier Foundation (EFF), Libreboot developers, and security expert Damien Zammit accused the ME of being a backdoor and a privacy concern. Zammit stresses that the ME has full access to memory (without the owner-controlled CPU cores having any knowledge), and has full access to the TCP/IP stack and can send and receive network packets independently of the operating system, thus bypassing its firewall.

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In the context of criticism of the Intel ME and AMD Secure Technology it has been pointed out that the National Security Agency (NSA) budget request for 2013 contained a Sigint Enabling Project with the goal to "Insert vulnerabilities into commercial encryption systems, IT systems, …" and it has been conjectured that Intel ME and AMD Secure Technology might be part of that program