Proximodistal development can be explained quite simply:
It is the trend of things beginning from the inside, the core, and then spreading outward. The word 'Proximodistal' comes from the latin, proxi - meaning close, and dis - meaning away from, therefore the word itself is exemplary of the trend, which is centrifugal (moving outwards).
The term is usually referred to in biology, which describes the process of more general functions of limbs developing before specific functions, such as fine motor skills. It basically describes the progress from the centre of the body (spine) to eventually mastering the more distant/peripheral parts of the body.
A fine example of this is to observe the way a baby first learns to control their shoulders before their fingers.
In the process of this development, motor skills at large take precedence over finer, more specific motor skills. A child will first experience control of their upper trunks, followed by arm control and subsequently finger control.
According to this principle, each change in the child’s development should result in an increasingly refined level of skill development.
The proximodistal law of development, however, is not confined just to biology. It is a universal principle. It's ideology, that everything starts in the center and works it's way outward, is the groundwork of many similar such theories.
Some examples include the Big Bang theory and the Chinese concept of Chi (energy force), which is a spiritual belief that begins with the self, eventually working it's way outwards.
I hope this answers your question.