Since a subplot is a story of its own, it should contain the five steps of any narrative—i.e., a story arc. Indeed, “subplot” may be a misnomer, more appropriately named “sub-story.” A subplot, then, must have a protagonist with a goal, who then takes steps toward that goal. Any secondary character in the main storyline (story A) without a separate project is probably not a subplot. Many secondary characters simply help the protagonist in story A, and no separate sub-story is being told about them.
To identify a subplot in your favorite story, simply ask whether character X has a goal and whether narrative is devoted to that character overcoming obstacles to reach it. For example, in The Hobbit, Bilbo, Thorin, and Gandalf each have distinct story goals. Bilbo seeks adventure and his share of the treasure. Thorin seeks to reclaim a throne. Gandalf seeks to prevent Smaug from allying with Sauron. By contrast, the individual dwarves under Thorin do not have a distinct story goal; they simply help Thorin achieve his.
Subplots can stem from the protagonist in story A. The protagonist can have more than one story goal: one for story A and one for subplot B. For instance, John could be pursuing a murderer, but also trying to repair his relationship with his son. Alternatively, subplots can stem from a secondary character in story A. John could be pursuing a murderer, while his son tries to rob a bank. Finally, a subplot can consist of the antagonist, who works toward a unique story goal. For example, the Senate Slayer plans to murder four politicians on July 4th. He prepares for it. The goal of John, our protagonist, is to stop him. John’s goal differs from the killer’s.
Now we have our layered narrative. John pursues a murderer (story A), who plans on killing four politicians shortly (subplot B). Meanwhile, John’s son tries to rob a bank (subplot C), on July 4th, where the four murders will occur, to everyone’s surprise.