Those of the shoot are usually protected by involucral leaves and the whole complex forms a bud. The apical meristems are the cause for tip growth which is one of the most striking features of vegetative growth. This contrasts with animal growth, which is an allometric process, i.e. all parts of the body grow in such a manner that its overall proportions are maintained. As soon as an animal has reached its final size, growth ceases. However, this does not mean that no cell divisions are taking place any more.
Cell divisions do happen all the time, especially in epithelia and in blood stem cells.
But this division activity always has the function of replacing old or damaged cells. Such repair does not occur in plants. If a leaf or flower or any other part is damaged it is neither replaced nor repaired. Rather are new organs are formed, and this again does not happen in animals. Dissect the shoot tip of Elodea under a stereo scope.