When your Mon is ready, all 3 of their Ancestors must be present in order for it to harness enough power to transform. Only a rare few species of the first generation of Mons can draw from their own power to transform without any ancestors.
To transform a Mon to its next highest form, you need to collect all of its Ancestors. When a Mon transforms, its level resets to 1 and its base stats reset within the higher point ranges associated with its new form. Higher forms also have generally higher growth trajectories, meaning some of your transformed Mon’s stats will now increase at a higher rate (e.g., 6 points per level vs. 3 points per level).
In general, higher form Mons are much more powerful than their lower form counterparts, especially as they reach higher levels.