When something or someone needs to be treated with kid gloves, this means that extra care is required. The term can be used to discuss a fragile or expensive object, or a situation which needs to be treated with tact and respect. It may also be used directly to refer to specific people, such as customers which are notoriously difficult to handle, suggesting that they need to be treated gently to avoid a scene. The colloquial term may also be used pejoratively, to imply mollycoddling, or excessively careful treatment.
The origins of the term date back to at least the 1800s. Kid gloves are gloves made from kidskin, the extremely soft hide of a young goat. The soft gloves were favored by members of the upper classes, especially women, in the 1800s because they protected the hands while also being soft and comfortable to wear. Since most of polite society wore gloves in the 1800s, finding comfortable and stylish gloves was very important. The soft gloves would also have felt gentle on the hands of others, reinforcing the idea that the wearer had smooth, touchable skin.
In the early 1800s, kidskin gloves began to be very much associated with the nobility and the elegant upper classes. Partially this was because the gloves would have been rather expensive, and not very accessible for other members of society. But kid gloves are also not very practical for hard or serious work. Since many upper class women in the 1800s projected a frail or weak image reinforced by society, kid gloves were probably linked with fragility and a need for gentleness as well.
The Oxford English Dictionary indicates that people were writing about the necessity for something to be treated with kid gloves by 1830, but the term may have been around before that. In the sense of a person or group of people, the term often refers to a potentially delicate or volatile situation. If the situation is treated with kid gloves, it can be easily and pleasantly defused for all. Fragile objects, of course, require delicate treatment because otherwise they will break.
When critics of a situation believe that it is being handled too delicately, they may suggest that the kid gloves need to come off. This is often the case with complex political situations which are not being handled directly and appropriately. A critic of such a situation might suggest that it is being treated with kid gloves because of political concerns like a desire to retain trading rights, to save face, or to hold a position in office.