I am biologist, plant biologist ... and auxins and their transport are my job to research.

Auxins are plant hormones responsible for shaping plant body and allowing plants to grow and react to the environment.

... Such a general statement of a function of one chemical class seems overly bold. However it is not too bold. (Maybe even understatement :-D ). Different plant cells do react quite differently to the same auxin at different times (this puzzled scientists for decades). Some start to grow, some stop to grow, some start to divide and multiply and other stop doing just that and yet others start to gain new functions. However actually all of them do react in some way or another. And it all comes down to the proper distribution of auxin between neighboring cells, the proportion of cells "own" auxin to that of the "neighbor's" auxin does matter as well.

Is there internal transport system within plant? Yes. There is.

And it is one of the wonders of Nature. While there exist also passive route of transport in the plant (being carried in the veins within the sap), it is the active transport - dubbed "polar auxin transport" which completely defines plant.

And I mean it. Without perfect spatio-temporal coordination of transport of auxin molecules between various cells within the plant body .. there would be no body, no shape, no growth. Auxin can be understood as a kind of unit of information in cell-to-cell communication. Different cells in a body have different task and they have to get the right task at the right position at the right time.

There are no nerves in plants. Yet even so the body still needs to be cohesive coordinated internally communicating unit.

How does it achieve it?

Slowly but surely - by exchanging, transmuting (metabolism) and perceiving units of auxin from and to their surroundings. (And to a lesser extent of other plant hormones too). This is self-organization of plant cells through the means of auxin as a medium of exchange.

Without this coordination - all the plant cells within body would be more or less the same and instead of body growing to the light and moisture - we would get unorganized heap of biological matter without capacity to survive on their own.

And yes all of this is driven by internal "delivery system". The delivery system in its own right is difficult to explain in detail. In short it is composed of various proteins on the membranes serving as directional pumps ... some are pumping in, some pumping out (of the cell) ... and all of them has different set of regulations from the other ones.

To know more .. try to google out "Polar auxin transport" and "auxin efflux carriers"