Active Risk is also known as tracking error.
An investment portfolio is subject to active risk as a result of active decisions made by a portfolio manager, who aims to 'beat' a benchmark by outperforming the benchmark's returns over a given time period. SeeAlpha
When a portfolio manager attempts to beat a benchmark, they will make reallocations to their portfolio which will alter the portfolio from the benchmark. Active risk is therefore a measure of deviation from the benchmark. Index funds have a zero active risk, as they follow an index and by definition do not deviate.
Active risk is calculated as the annualised standard deviation of the monthly difference between the portfolio's return and the benchmark's return.