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Seriously though, if you can visualize the base on a transistor as a lever
that you push on (with small current) the other end of the lever pushes harder (more current) so with a small current that you sink into the base you can use that as a lever to control more current on the collector emitter junction.
I have also had to explain it this way, to students, think of the collector-emitter junction as an electron controlled variable resistor, put more electrons into the base and the resistance drops in the collector-emitter junction causing more current, less electrons into the base and the resistance raises causing less current.
Since Ohm's theory says V=IR then that is how you get a swing in voltage in the output circuit, the base-emitter junction starts "turning on" at .6Vdc and is fully on at .7Vdc, so if you vary the base voltage from .6 to .7 then you can control the current in the collector-emitter junction from idle current to full current.