The protagonist has seen his life move from one phase to another repeatedly, and he has realized that with each change (which he describes as the end of fall of the old phase), he needed to find a new place in the world.
When plants grow, we change them to a bigger pot from time to time. If we do not do that, the plant will be unable to grow further, because it cannot extend its roots.
Thus, by transplanting the plant, we enable it to grow.
In a similar fashion, we need to transplant ourselves as we move through the phases of life, we need to find a new place (physically or metaphorically) to extend our roots to enable growth.
That transplantation may be physical, as in moving to a different city, but it is more likely meant in a metaphorical way. As we grow up, our role (and thus place) in society changes.
We take on new responsibilities, we make new and different kinds of friends, and we may well feel we are in a different place altogether.
That displacement can cause uneasiness, doubt, maybe even pain or shock. But as the author states, it is necessary that this changes happen, for they enable us to grow.