I recall reading how BJT works in an old book when i was about that age. It was explained that it would normally not pass any current, as two diodes would not, but as the base is so thin, injection of other type of charge carriers into the base by making one of diodes conduct current makes the second diode leak."children"??
If you really mean children then, apart from saying that a transistor acts a bit like a variable resistor with its value controlled by the third connection, what would be the point of anything more? If you're using terms like "potential barrier" then what sort of children would you expect to be familiar with them?
Frankly, I think that just describing a common base amplifier, and how the signal becomes inverted, would be way too hard for most kids of secondary age (except a few enthusiasts who already have some experience of making up circuits). They may well be impressed with seeing an amplifier actually operate but, as for 'understanding', I doubt it.
What are the circumstances in which you are hoping to present these ideas?
I remember my Dad, in a one-to-one situation, explaining successfully (as I remember) how a thermionic triode works when I was about 11 yrs old. The triode is a much simpler device to describe and, being called a 'valve' it even sounded a bit like a tap.
It previously explained how diode works with charges being pushed away from midline, and had a drawing of transistor with charges.
Not a very accurate explanation I know, but it made sense to me back then, and is not grossly invalid.