The phrase built off is another way of saying built on, which means adding on to something that already exists.
As the inventor of C++, Bjarne Stroustrup, explains in one of his books, he added Simula-style classes to C to create "C With Classes," which became C++:
I originally designed and implemented [C++] because I wanted to
distribute the services of a UNIX kernel across multiprocessors and
local-area networks (what are now known as multicores and clusters).
For that, I needed some event-driven simulations for which Simula
would have been ideal, except for performance considerations. I also
needed to deal directly with hardware and provide high-performance
concurrent programming mechanisms for which C would have been ideal,
except for its weak support for modularity and type checking. The
result of adding Simula-style classes to C, “C with Classes,” was used
for major projects in which its facilities for writing programs that
use minimal time and space were severely tested. The name C++
(pronounced “see plus plus”) was coined by Rick Mascitti in the summer
of 1983 and chosen as the replacement for “C with Classes” by me.