Telling:
I opened the letter and smiled as I read. When I finished, I put the letter in my pocket and walked back to the house.
Okay - so what's wrong with this picture? There isn't one. Does this really draw me into the scene or give me basic references to visualize one? Not really.
Showing:
I turned the letter over and slipped my fingernail between the flap and the M stamped seal to break it open. The corner of my mouth curved upward as I read. I folded the letter and returned it to the envelope.
This example gives the reader a lot more information that offers plenty of references to visualize the scene. First off, The fact that the letter is stamped with a seal indicates a specific time period. Instead of saying I smiled, the writer describes how this person's lips moved. Showing actually provides more information that paints a more complete picture for the reader.
This is a technique that requires constant scrutiny. The writer needs to always ask the what and how of everything. How does the smile look? How did the character walk back to the house. Did she stroll or trot or take a brisk pace?