Towels
This is probably the most obvious possibility.
Hang a dish towel or hand towel from the rod so it’s always within reach of the sink.
Aprons
If you use an apron while cooking, the rod could provide a convenient place to hang it.
Reusable Shopping Bags
The rod could also work as a simple storage spot for lightweight reusable bags.
Cleaning Cloths
Small towels and cleaning cloths could be hung there to dry.
Oven Mitts
If the mitts have loops, they could potentially be hung from hooks or clips