Parboil is to boil a food just until it is partially done.
What “partially done” means depends on the food item, and the use it will be put to in a given recipe.
It generally implies a longer cooking time than parblanching or blanching, though sometimes the words are used interchangeably, and less of a cooking time than boiling.
The process is used to prepare vegetables for canning or freezing. It helps to destroy enzymes which would otherwise cause the food to deteriorate in storage. Some recipes will ask you to parboil carrots and cauliflower before canning, others will give you the same directions, but call it blanching.
When the term is applied to vegetables, it’s usually denser vegetables such as root vegetables, and is often used for an item whose cooking will be completely using another method. In Parboiling longer-cooking time items, you give them a head start so that they can then be cooked with items that take less time, or so that, as when roasting potatoes, a cooking method can be applied to them that would turn the outside to ash before the inside was done.
When Parboiling, you have a quantity of boiling water, large in comparison to the amount of food items you are going to parboil in it. This helps prevent the temperature dropping and the boil being lost, which would throw off your counting time and possibly cause the food item to be cooked too much, or even completely cooked.
Sometimes a recipe will then ask you to transfer the food items immediately into cold water. If further cooking is going to happen right away, you’ll just be asked to drain the food items.
To parboil potatoes, put them in cold water, bring to the boil, boil for 5 minutes for small potatoes, 7 minutes for larger ones, then drain.