Statistics borrows the term for the count of values free to vary. In strategy research it is a rough accounting of how many knobs you turned, including the ones you turned and then turned back.
A useful ratio is trades per degree of freedom. With 500 trades and 5 parameters you have 100 trades per knob, which is thin but workable. With 500 trades and 20 parameters you have 25, and the backtest is largely a description of those particular 500 trades.
Count honestly. Trying six indicators and keeping one is six degrees of freedom, not one, even though the final rule mentions a single indicator. This is the same problem as multiple-testing.
Related: parameter, overfitting, multiple-testing, sample-size