New cells are born at the growing point or apex of a plant. They are created by the division of the meristematic cells in the apical dome.
In its simplest state (at this point in time still an embryo) the wheat plant has two meristematic domes where new cells are produced. One is at the tip of the shoot and the other is at the tip of the root. The shoot tip meristem starts off by producing cells whose eventual fate is to become leaves. Together, a group of these cells is called a leaf primordium. Whilst leaves are being prepared the apex is said to be vegetative. Later the meristematic dome will produce cells whose fate is to become parts of the flower.
In winter wheat this process takes place during the late tillering phase when the growing point is buried beneath the soil surface. If you dissect away all the green leaves from a tillering wheat plant eventually, at the centre, you will find the shoot apical dome. Under a microscope this structure is very beautiful and we can watch it as it changes from leaf production to flower production.