Edited from wikipedia:

A mechanical room, often referred to as a  boiler room or simply the plant room (in the energy modeling world, it seems "mech room" or just "mechanical" is the descriptor). It is a room or space in a building dedicated to the mechanical equipment and its associated electrical equipment, as opposed to rooms intended for human occupancy or storage.

The Mechanical room usually is locked or has a sign on it that says "Staff only" or even "Danger". There are many components in a mechanical room and usually you can hear noises from the room such as fans or pumps.

It is not to be confused with the Janitor's closet which usually just has tools and a mop in it.

If you enter a mechanical room, you'll often see various equipment and panels, pipes hanging from the ceiling. If the building is old, you often see a combination of new and old equipment which is nigh impossible to understand except for the building operator.

There are often high voltage panels in mechanical rooms and plenty of places to hit your head and hard hats are often encouraged.

Unless a building is served by a centralized heating plant, the size of the mechanical room is usually proportional to the size of the building. A small building or home may have at most a utility room but in larger buildings, mechanical rooms can be of considerable size, often requiring multiple rooms throughout the building, or even occupying one or more complete floors 

A home equivalent of a mechanical room is a room where your furnace and/or air conditioning supply is kept. It can be as small as a closet in many cases.

In Hollywood movies, a mechanical or electrical room is often featured in a "chase scene" where the protagonist enters/escapes through a duct or a pipe and/or by cutting the power to the building. Here's a youtube example. 

Attached is a picture of AI art generated by "Person giving tour of Mechanical Room"
AI obviously has never been on a tour of a mechanical room, but this one has that dark ominous look that many mech rooms have.