"herba" means in the most cases the aerial parts: that means all aboveground parts that are harvested as medicine, often just before or during flowering. Examples include spilanthes (Spilanthis oleraceae herba) and St John’s wort (Hypericum perforatum; Hyperici herba).
There is also "herba tota" which means the entire plant, so the whole plant is used, roots and all (e.g. Taraxacum officinale herba tota).
For the exact definition you have to look into the European pharmacopoeia for example, there is it described for every herbal medicinal product. These are terms from pharmacopoeias.