When you do something equitably, you do it fairly or in an equal, impartial way. To share a pizza equitably, you need to give each of your friends the same number of slices.
In an ideal society, people would be equitably paid for the work they do: men and women would make the same wage for doing the same job, for example. Most fair-minded people try to treat everyone equitably, although most of us tend to give special preference to those we love and care about. Equitably comes from the French équitable, "equitable or fair," ultimately from the Latin aequitatem, "equality, fairness."