Telling and showing are important tools in your writing.
When I sent out my first manuscript, I got a very nice rejection letter from an agent who praised my writing but said I needed to show more and tell less. I didn't have a clue what she was talking about.
Since then, I've learned the difference between showing and telling and how critical it is. It's like the difference between "feeling" and observing a "feeling."
Look at these examples:
“Susan was paranoid.”
“Susan felt their eyes on her even when she was alone in her bedroom. In a restaurant, she knew they were behind her. She could feel and smell their rancid breath on her neck and hear their scornful laughter. She worried they might have put something in her food when she wasn’t looking. More than once, she had swung around quickly but she could never catch them.”
The first one, "Susan was paranoid," is telling. We can't feel what Susan is feeling, but in the second example we experience it as she does. The passage is longer but it generates emotions. We can smell, hear and taste her fear. It shows how she feels. We're witnessing the story.
As Robert McKee says in his craft book Story, “We render the precise experience necessary to cause emotion, then take the audience through that experience.”
That is showing rather than telling.
The problem with telling is it's too abstract. We can’t feel the emotion the character is supposedly feeling. The writer is telling us about a frightening event instead of bringing us into the scene and engendering emotions inside us. The closer you let us get to the action and to the characters the more powerful your story will be.
Does that mean you should never tell? There are plenty of times when it's more appropriate to tell than show. When there is not enough going on to generate a scene, it's okay to describe. When you want to pass rapidly through time, tell us. Use such phrases as "Two weeks later..." and "The day after the fire..."
As the storyteller, your job is to create events that have conflict and emotion inherent in them. When you do that, you won’t need to “tell” us how your characters feel. You will “show” us, and if the conflict and emotion are universal and as strong as they should be, we’ll be transported into your characters' world.