Your hand is covered in dirt, ink, mud, sometimes an unidentified substance. You try to wash it without fully succeeding.
The emotional tone
A persistent discomfort, a malaise that sticks. Sometimes shame, even if the source of the dirt is unclear.
Symbolic meaning
The dirty hand carries the trace of an act consciousness hasn't digested, not necessarily serious, sometimes just a sentence said too fast, a silence not kept. It symbolizes what stays stuck to our way of acting.
The palmistry link
Palmistry reads the palm as a register. A stained hand in a dream evokes momentarily obscured lines, recent choices you haven't yet inwardly recovered from.
What this dream signals in your life
This dream often returns after a poorly closed conflict, or after doing something against your values. It demands repair, not punishment.
You don't wash a dirty hand in a dream. You wash it awake, by changing something.