With regard to readers connecting to a piece of writing, "shared personal experience" relates to how our words, no matter what we write, connect (or don't) with our readers. It's always about authentic emotion.
How do we do this? Two main ways. First, through specific language: examples, descriptions, images. Second, through relatable characters or narrated experience.
Ecclesiastes tells us (and Shakespeare's Sonnet 59 extends the metaphor to creative work) "there is nothing new under the sun." While the details change, all feelings have been felt, all experiences experienced, all ideas ideated.
So what makes some words resonate while others fall flat?
Well, what is it that changes? Details. Specifics.
My experience and your experience and someone else's experience bear only the resemblance of basic facts: this happened to me. Me too! But all individuals think, feel, act and react uniquely. That, my friends, is the clearly stated specific language through which we, and our readers, connect.
A character's first day on the job might include an alarm that doesn't go off, a spilled bowl of Chex down nice linen trousers, a broken heel, and missing the bus by mere seconds. For a reader to relate, it isn't necessary that they intimately know the experience of spilling milk on their clothes before an important event or even of being late. Rather, the specific experience of becoming aware that we all lack control more than we like to admit, or perhaps those times when it seems the universe is out to get us...that's what resonates.
The universal is never what leads a reader to connect it to their personal situation. Rather, the personal — the specific, unique language that accurately describes exactly what you mean, not in spite of the fact that it differs from that of your reader, but because of that difference — connects. Our minds, usually subconsciously, fill in our own personal details and experiences, "replacing" the written description.