I have to look up botanical definitions all the time.
Here's more of the petiole description from CATE.
"...usually obtusely and sharply to weakly flattened near apex, narrowly rounded to broadly convex abaxially winged on lateral margins, the wings usually prominently undulate (especially toward apex),..."
From the description the petiole is not circular in cross section. It's flattened near the top and oval to convex lower down. Since it's not circular, I believe
lateral margins refers to the sides of the petiole. The wings (one to each side)
are the "serrated edges"
Wings undulate means they are wavy. Those pics on the Nature Love You Site you linked show it really well. Look at photo DSC07515 (15), second from last. This can look serrated from a distance.
