Stirring food in a pot helps it cook better and more evenly, and therefore one who stirs food that is not fully cooked on Shabbat transgresses a Torah prohibition. The act of stirring is known in rabbinic literature as megis. Even if the food is no longer on the fire, as long as it is not fully cooked and it is yad soledet bo, it is forbidden by Torah law to stir it. In light of this, the Sages forbade removing food from a pot that contains food that is not yet fully cooked, even after the pot is removed from the plata, because the resultant movement in the pot would constitute stirring. Only when the food has cooled down and is no longer yad soledet bo may one remove the food he wants.
However, once the food has finished cooking and is ready to be eaten, there is no longer a problem of Bishul, and one may remove whatever he wants from the pot (SA 318:18). This is the custom of many Sephardim. In any case, one should not stir the food while it is still on the fire, because this resembles cooking (Yalkut Yosef 318:43).
The custom of Ashkenazim and some Sephardim is to be more stringent. As long as the food is still on the plata, even if it is fully cooked, le-khatĥila they do not remove any food. Rather, first they remove the pot from the plata and only then remove what they want. If they wish to return the pot to the plata afterward, they must be careful to follow the principles for returning food to the plata (section 19 below).
In cases of necessity, even those who are usually stringent are lenient, and allow fully cooked food to be removed from a pot on the fire. For example, if a pot is resting on an uncovered fire, so that if it is removed from the fire it will be forbidden to replace it (see section 19), one may remove food from the pot while it is still on the fire. This is because technically once the food is fully cooked there is no longer a prohibition of megis (Ĥazon Ish 37:15; SSK 1:38). Everyone agrees that if a pot or metal urn is filled with boiling water before Shabbat and then left on the plata during Shabbat, one may remove water from it on Shabbat (SSK 1:39).