The distinction between showing and telling is vital. Over the long haul, it's the difference between the reader being inside the story, experiencing each moment, and being outside, getting just the gist.
You can “tell" the reader about a character with direct statements of fact and interpretation, like this:
At the party, Melissa was in a foul mood and the revelers annoyed her.
It's more dynamic and interesting, though, to let the reader “see" Melissa's foul mood and annoyance for himself:
When a gaggle of girls half her age came out on the balcony to smoke, Melissa made her way to the sliding glass door, shoving past the one in a strapless dress and shamelessly high heels so that the girl had to grasp onto her friend's shoulder to keep her balance.
Here, the reader is standing out on the balcony with Melissa, acting as witness and making interpretations and conclusions based on what unfolds. This provides a deeper understanding of Melissa's personality, too. Another character might have shot silent glares when her sanctuary was taken over. Still another might have let out an open mouthed roar at the gaggle of girls.
Let's take a look at another example. In Tim Gautreaux's “Dancing with the One-Armed Girl," Iry stops his car to pick up Claudine, a hitchhiker:
"You need a ride?"
"Yes." She was pale, late thirties or so, with dark wiry hair spiked straight up in a tall, scary crew cut, and tawny skin. He thought she looked like a woman he'd once seen on TV who was beating a policeman with a sign on a stick. She seemed very nervous. "But I was hoping for a ride from a woman," she said.
"I can't afford no sex-change operation," he told her. "That your car?"
She looked back down the road. "Yes. At least it was. A man just pulled off who made all kinds of mystifying mechanical statements about it, saying it'd take three thousand dollars worth of work to make it worth four hundred. I guess I'll just leave it." She sniffed the air inside the Jeep. "It's awfully hot and I hate to pass up a ride."
Claudine's apprehension is imbedded in her actions. It's in her dialogue, too, when she tells him she was hoping for a ride with a woman. At the same time, she's rather chatty, talking about the man who made “mystifying mechanical statements," and she's weighing the dangers of a ride with Iry versus sitting out in the heat. So, she might be hesitant, but she's not terrified. The collection of specific details, action and dialogue reveal precisely how Claudine feels, much more so than a more general line of telling could. (There's much more that's shown in this passage, too, including the great description of Claudine. In just two sentences she springs to life.
The oft used phrase “show, don't tell" might leave some writers feeling like there's no room in fiction for telling. That's not true. It's a useful and succinct way to share information the reader needs to know. Still, you should rely mostly on showing. Let the reader inside the story to experience each moment just as the characters do.