It means that he supervises the construction.
This meaning exists in English, and in Latin.
It means to pile up (first literal meaning), to build, to construct and to erect.
When you erect something for instance:
Gustave Eiffel erected the Eiffel tower and the Statue of Liberty.
He did that as an architect, not a worker, or it would have been a lot of work!
(I don't remember a lot of well known architects, I should study more this topic)