How do I write the passing of a few years in a story? I have two separate character timelines and I want to show the characters aging throughout the story. Should I divide it up into parts? You can read what I have of my story here to see what different segments I'm working with and get a better idea of what I'm asking.
One way to show passage of time is by referring to time-based events. Over the course of a year you can use seasons for this; if we see your characters walking through the snow, and next see them walking through the fall leaves, we know that at least half a year has passed. For multi-year spans, look for milestone events: a graduating student who we last saw entering college, somebody celebrating his five-year anniversary at the job, the birth and progress of children (could be relatives/friends and not your characters), the first fruit from the tree they planted as a sapling in the earlier part, whatever works in your story.
Another way, if you're using the close-character POV, is to use your characters' thoughts: "Had it really been three years already since (prominent event from the earlier part)?" and the like.
The key word in your little conundrum is "context". Remember the basic elements of plot; setup, conflict, resolution.
The setup is just that; you set everything up. Now understand that each new "timeline" is essentially a different context with a new setup. What Monica above suggested with the seasons is essentially a way of signaling the reader that things are "different" in a way that can't be explained other then the passing of time.
You don't get autumn leaves in the springtime, nor snowfall in the summer. You don't watch the wrinkles on your receding hairline at age 15 nor do you pop pimples when your 6.
Your task is this; think about what features each timeline has that is both distinct and readily apparent to the narrating character. Then you must describe them in a way that is concise and relevant to the story.
Use these descriptions to separate them in your story. Consider breaking it into parts, like chapters or sections, with said descriptions beginning each part. Also consider just naming the time and date between each timeline. Separating them is important, and you need to figure out how you want to do that. Breaking it apart is just one possible solution.