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One way to describe a transistor is to describe it like a tap. If you think of a normal garden tap, but instead of the normal tap handle you have a wheel which can be turned on by water flowing into it. So when the current/water flows through this wheel it turns on the on the tap and allows a large amount of water to flow out of the main part of the tap. Because the amount of current/water flowing out of the main tap is very large compared to the amount flowing into the wheel it is like the water\current is amplified.
In a real transistor the wheel that turn on the transistor is called the base. The pin that the big current flows out of (tap) is called the emitter and the pin that the big current comes from (house plumbing) is the collector.
This is a fairly simple description for a relatively complex component, but I hope it explains the basic function of a transistor.
The basic transistor formulas are
Current into the base x factor(normally called beta) = current out of the emitter
Current into the base + current into the collector = current out of the emitter
The important thing to remember with transistors is that they are current devices and that voltage hasn’t got a lot to do with the operation of the transistor.
I hope that has helped (and hasn’t confused too much), if you still have questions or if you want a more scientific description then please ask.