? wrote
This year I bought a banana plant. It is growing well, though no
flowers or fruit yet, but a number of little banana plants are growing
from around the base of the big plant. Am I able to transplant these
into new pots and grow new banana plants? Is the plant reproducing, or
are these shoots just new "branches" of the big plant? I'm reluctant
to start digging in case I damage anything.

That's the way they grow, into a clump, but the individual plant dies after
fruiting leaving the younger ones to grow and do likewise, etc, etc.....
To take them off and pot up separately you will need to ensure each little
plant has a root attached before severing it's attachment to the "mother"
plant.

--
Regards
Bob
in Runnymede, 17miles west of London, UK