Climbing gloves allow you to grab onto any type of wall and climb up them or abseil down them as if it were a ledge. This allows you to reduce or prevent fall damage, lets you grab onto ledges one square higher than normal, and reach some areas that would normally need a rope to access.
However, even with climbing gloves, there are several situations where you may need to use a rope, such as climbing up overhanging ledges or descending caverns that have no walls for you to cling to, such as in the Ice Caves.
Climbing Gloves can be equipped at the same time as the Pitcher's Mitt and work especially well when used with Spring Shoes and a cape.
They are made virtually redundant with a jetpack, but will still help with managing fall damage and conserving jetpack flight time.