Telling: “Close the door,” she said nervously.
Showing: Her cigarette trembled in her hand: “Close the door.”
Telling: Peter was a fussy, neat sort of man.
Showing: Every Monday, Peter ironed and folded his towels into perfect squares and stacked them in the airing press, according to size and colour.
“Showing” your reader what your protagonist is thinking/doing, encourages your reader to engage more with your book/story/play, to interpret and picture what is going on. Showing also allows for more atmosphere and lends insight into character. Conversely, “telling” tends to deliver all the information neatly wrapped and can deny the reader all the fun of involvement and imagining. Therefore, rather than telling the reader, ‘Bob was depressed,’ you might describe what Bob was doing and saying and the reader will also get a greater sense of ‘Bob’ if you do so.
Having said that, if the writer “shows” every inch of their novel it may bore the reader and slow the pace. There are times, for the sake of speed and economy, the writer needs to “tell”, so they can quickly move on to the next stage of the story.
If I could suggest a rule of thumb, it would be “show” the most important parts/events of the story and “tell” the minor linking passages. It’s your judgement call as to when and where to show or tell, but do give it thought. Finally, please bear in mind the general consensus is that you always avoid telling via adverbs in speech attribution: “he said arrogantly”, “she shouted defiantly”, “we mumbled apologetically”. Instead, try to think of ways you could show this arrogance, defiance or apology.