What is meant by "plant" in control system?

It could be anything that has an input and gives an output. In control theory is depicted as a box with a relation Output VS. Input, we call this transfer function. It may have also multiple inputs and/or multiple outputs.

The physical size is not important, so yes your DC motor could also be a plant.

Indeed, as Marko writes, it can be just a DC motor. In general it's "the thing being controlled".

In fact the word "plant" in plain English can mean

• "factory", as the OP points out (Cement factory)

and closer to the field of control theory it can also mean

• "machines", without the factory building

For instance "the heating plant for a home" or "nuclear plant for a submarine"; https://www.dictionary.com/browse/plant

I'll let the linguists battle it out, but it does origin from the word for "shrub", which rooted in soil, with branches, leaves etc.. and if you look at a power plant or heating plant, they look like that too: mounted to the ground, with protruding tubes, boxes etc.... so maybe plant -the machine- came before plant -the factory.

See also the comment by Ross, who found the etymology back to the 18th century: "at first with reference to the machinery, tools, apparatus, etc., later also the building"

There's something that connects the non-mobile machine, installed at a factory, with feed pipes, exhaust pipes etc..., with the rooted, and thus obviously non-mobile, plant.

And according to Andrew (see comments), in British English it's quite common to refer to heavy and mobile machinery like bulldozers, graders, and road rollers as "heavy plant"

Image: https://thoughtsbyanidlemind.wordpress.com/2013/02/15/thoughts-on-heavy-plant-crossing/