Order of flowering

Good question. The reasoning behind it has to do with sexual reproduction. 

Many flowers have evolved very specific associations with a particular insect species or group of species. In these cases flower structure may be very specialized Orchids, Foxgloves and Primroses, Buddleja (butterfly bush), show a range of adaptations to insect pollination. 
Order of bloom being one. 
There are variations... Gladiolus for example, blooming bottom to top,  flower spikes are bisexual flowers.
Bisexual being flower of each individual has both male and female structures,  combining both sexes in one structure. flowers of this kind are called perfect, having both stamens and carpels. Therefor the plant is capable of self pollination.

To give you a direct botanist type answer the pattern of flower blooming you are referring to is called inflorescence.
An inflorescence is a group or cluster of flowers arranged on a stem that is composed of a main branch or a complicated arrangement of branches.

Morphologically, it is the part of the shoot of seed plants where flowers are formed and which is accordingly modified. The modifications can involve the length and the nature of the internodes and the phyllotaxis, as well as variations in the proportions, compressions, swellings, adnations, connations and reduction of main and secondary axes. Inflorescence can also be defined as the reproductive portion of a plant that bears a cluster of flowers in a specific pattern.

Inflorescences are described by many different characteristics including how the flowers are arranged on the peduncle, the blooming order of the flowers and how different clusters of flowers are grouped within it. These terms are general representations as plants in nature can have a combination of types.

Plant organs can grow according to two different schemes, namely monopodial or racemose and sympodial or cymose. In inflorescences these two different growth patterns are called indeterminate or determinate, and indicate whether a terminal flower is formed and where flowering starts within the inflorescence.

In determinate inflorescences the terminal flower is usually the first to mature (precursive development), while the others tend to mature starting from the bottom of the stem. This pattern is called acropetal maturation. When flowers start to mature from the top of the stem, maturation is basipetal, while when the central mature first, divergent.

O.O ... I'll stop here and not go into catkins, spikes, umbels, etc. But, there's your answer. Inflorescences.