When your fingers are slippery, you drop any non-cursed weapon you were wielding (which can be problematic in a shop). If you are not wielding a weapon, or you are wielding a cursed weapon, your non-cursed rings may slip from your fingers. Applying a towel effectively cleans your fingers. Putting gloves on does not remove or cover this effect, due to forces of physics yet unfathomed. The lesson here is to watch exactly what it is you are eating/applying, as slippery fingers can very easily lead to a swift death if said tin or grease was used out of pure necessity.
As of NetHack 3.6.0, stir fried food from a tin can also cause slippery fingers.