Your question is about the fundamental operation of a BJT. Surely there is much written about that out there.
Briefly, C-B-E is a sandwich of three semiconductors of opposite polarity doping. However, what makes a BJT more than just two diodes in series pointing in opposite directions is that the base region is so thin that the depletion region of each junction extends to the other junction. The collector is still within reach of the emitter, if it weren't for the base region in between with all its carriers depleted. A little bit of externally applied base current injects carriers into the base region, which now allows current to flow accross it between collector and emitter.
Due to a whole bunch of semiconductor physics you should look up elsewhere, a few carriers in the base go a long way. This is where the transistor gets its gain from. You inject a few carriers into the base (provide a small base current) and that lets a lot of carriers conduct (allows a larger current to flow) accross the otherwise depleted base region between collector and emitter.