For a sample mean, sigma / sqrt(n).
The consequence that matters: halving your uncertainty needs four times the data. This is why validating a strategy takes years rather than months.
Do not confuse it with standard deviation. Standard deviation describes the spread of the data; standard error describes the precision of a statistic computed from it. Standard error shrinks with more data; standard deviation does not.
For a Sharpe ratio, the standard error is roughly 1/sqrt(years) - so distinguishing a Sharpe of 1 from zero takes about four years.