The example of this that professor used was a great Lorrie Moore story, "You're Ugly, Too." In it, the main character has a host of small, rather familiar problems — lonliness, being isolated as the only woman in her workplace, trying to make romantic relationships work. All of this is good stuff. What really keeps us turning the pages, however, is an almost passing reference to a lump discovered under her skin that has to be biopsied. For much of the story, we're waiting for the results of this biopsy. It isn't the main point of the story, and it doesn't return again and again, dogging our steps. And yet we want to keep reading because it's one more reason to feel tension and to be worried about the health of and welfare of this character we've come to care about.
To make your story that more engaging, try introducing a small, nagging source of tension or suspense. Your character might be fired from his job soon, or is slowly sinking into debt. Whatever it is, it's not the main pull of your story, but it makes the main plotlines stand out more clearly because they are defined by a charged timeline of worry and climax. Something's going to have to happen about that debt or that job or that cancerous-looking mole. It's the kind of thing that keeps the wheels of a story turning.