The reason distinguishing between people and things is useful is related to something called 'animacy' (or how active something is).
'People'—which includes most animals, as well as humans—are highly animate. People have control over their behaviour and act on their environment. They can run, jump, speak, shove, decide, eat, dream, do...
'Things'—like plants, furniture, ideas, rocks, and so on—are mostly inanimate. Things exist in the world and are affected by the actions or existence of other entities (people or things). They sit, float, grow, rustle, collapse...
One very effective tool you can use in your writing is to simply use a more active verb (like 'run', 'jump', etc.) with a thing.
Compare these two sentences:
- Lucy hopped.
- The stream hopped.
It's easy to imagine what Lucy looks like (a girl bouncing up and down on one leg), but what does a stream hopping look like?
It's probably quite energetic; there would be water splashing around, and maybe a lot of bubbles on the surface. You might even start to attribute human qualities to the stream, like excitement, or eagerness.
The description is made more evocative by taking a verb that normally applies to people and using it on a thing.