The Treynor index is a risk adjusted measure of portfolio performance, not unlike the Sharpe ratio. The Treynor index only adjusts for non-diversifiable risk, by dividing the excess return by the portfolio beta:
(rp - rf)/β
Where rp is the return on the portfolio,
rf is the risk free return, and,
β is the beta of the portfolio.
By excluding only adjusting for non-diversifiable risk, we assume that the portfolio it self is an investment that we expect to be part of a wider diversified portfolio. As this is typically true for funds this means that it is a suitable measure for assessing the performance of fund managers.