What does it mean if your palms are peeling in places?

Past inflammation...: Fingers or palms can peel skin at the topmost layer if there was some inflammation (such as a recent fever or viral infection), some 1st degree burns (such as hot coffee), some blistering or non-blistering friction (such as digging with a shovel), some eczema or allergic skin reaction, some chemical or irritant reaction, a sunburn, etc... If peeling persists, a dermatologist can check the hands.

Peeling: Though it is usually dry skin, a disease called dishydrotic eczema can cause it as well. Cortisone cream often helps as well as moisturizers with lactic acid.