The entire story of Gone Home follows Kaitlin as you walk her throughout the house finding journal entries. This postcard could be considered the final piece of the puzzle that ties up all loose ends when it comes to where Sam went. The postcard is written to Kaitlin from Sam, just like the first thing you see when you begin the game.
As many can imagine, leaving your entire family out of nowhere would be quite difficult emotionally. The idea of the postcard plays on that. The letter is a way to ease Sam’s mind after her decision to leave home. Although the main reason why Sam left the way she did was to escape her current life, she still wanted to let at least part of her family know what happened. It is known through the letter found on the door that Sam doesn’t want her parents to know anything about why she left or where she is, and this is mirrored by the post script at the end of the postcard.