Active self introspection is the idea of investigating our own emotions, thoughts, behavior and conduct, and meditating on ways to avoid self-deprecating acts. For e.g.: If we are at loggerheads with someone, rather than carp or cavil, Hindu scriptures advises us to self introspect and realize that it is a reflection of our own shortfalls. It might be because of our own selfishness or ego that we are failing to see the other person's point of view, it might be because our own self aggrandizement that we fail to respect the other person, or it might be because we are attached to a desire / goal, that it blinds us of objectivity. If we acknowledge the fact that all of us are creation of God, and that no one is superior to other, and that it is superior in fact for humans to respect and accommodate the other being, it would be easier to break the ice.
Another example where self-introspection could help enhance our effectiveness is, when we feel we truly deserved the much awaited fat hike / career advancement, but it is awarded to someone else. The immediate instinct is to brood over the partiality, unfairness, and loathe the superiors, peer etc. But if we accede to the the teachings of Hindu scriptures, and introspect, we might unearth hidden gems. Foremost, it will help us attribute the success of the person who obtained it, to the value that the person brings. This then paves ways for us to identify our shortcomings. It might be that the inter-personal skills needs improvement, it might be that a better business acumen is essential, it might be that there is a need to change the role / domain where our strengths shine etc.. This kind of objective evaluation of the situation lends to better decision and improves our chances of landing that prized hike / advancement, or might be even better.
In essence, self-introspection leads to change that which is in our direct control - our own thoughts, behavior and conduct, which is what will lead to true effectiveness. We can continue blaming others, blaming our misfortune etc. , but that would not help us an ounce.