When you boil the water it changes from it’s liquid state to a gas state (steam). The coffee particles, however, do not change state, they stay a solid. The water steam rises by itself leaving the coffee molecules behind, so when you cool it back into a liquid state it is pure water again. This is the same process used for desalination (getting the salt out of salt water).
This works because coffee, salt water, etc are mixtures of two compounds, and so can be separated by physical means.
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