A fully funded program is maxing out scholarship allotments as dictated by the NCAA. As already stated, 12.6 for men and 18 for women.
As far as how it correlates to team success and individual athletes that varies. You can be a walkon on a fully funded team, it just means that the 12.6 and 18 scholarships are going to other athletes. Academic scholarships do not count against a team's scholarship count...most of the time. Scholarships can be divided and indeterminate amount of athletes, but a school must not exceed the maximum equivalent of scholarships, i.e. a school could give 36 women 50% scholarships.
Chances are a fully funded team is going to be more competitive. But, just as there are good teams from small conferences and bad teams from power conferences, there will be good teams that are not fully funded (especially at the DII level) and some lackluster teams that are fully funded. There is more to the equation than just scholarships; coaching, admin support, facilities and operating budgets also factor into the strength of a program. But chances are that a team with scholarship dollars, especially in men's track and field, has the administration behind them as well as a good operating budget.
Also, full equivalency amounts at the DII level are 12 scholarships for both men and women. (I think that's right, correct me if I am wrong.)