First, we should define "average reader." This might be tough. We don't want to be disparaging, nor do we want to glorify the "average reader" (which is disparaging in its own way).
Perhaps we could say that the average reader is ordinary. We don't mean that as an insult. What we mean is that the average reader might not have an extraordinary amount of college degrees, an uncommon knowledge of literary theories, or a rare understanding of literary or artistic ideas.
We might say that Gioia's poems are accessible to this hypothetical "average reader" because his poems are usually about things that most humans experience.
Let's look at "Finding a Box of Family Letters." What's this poem about? It's about Gioia looking at his departed parents' letters and photographs. This is not an obscure or unique activity. Lots of people do this, so we see why it could be deemed an accessible topic.
Let's look at one more poem. How about "Cruising with the Beach Boys"? In this poem, Gioia is driving around in a "rented car" when he hears a song that makes him think about the times when he was younger. Again, this is not a rare situation. All of the time, people hear songs that start a surge of memories or recollections.
Again, when we read Gioia, we continually see how the topics he chooses are those that don't require special training or knowledge. Perhaps this universality is the main ingredient that makes him accessible to the average reader.
However, I would encourage you to look at poets that are portrayed as not so accessible to the average reader. When reading their poems, I'd encourage you to ask yourself if these poems are really as difficult and oblique as teachers, scholars, and others make them out to be?