Common Emitter. Why and how to

Common Emitter is an expression to indicate exactly an electrical configuration where a part on three of BJT transitor (and only that kind of transistors) is used as reference for the other two.
So keep in mind it's impossible to make confusion with other contexts.

But... what's an emitter, or a transistor? why bjt? I'm instead confused!
And you're right if never seen one of them, neither in theory exposition.

Generally a transistor is a semiconductor device which you can regulate voltage and/or current in output with; maybe its name's explanation could give a bit of information more: transistor is the contraction of "transfer resistor".
According to their inventors it's been so called "because it's a resistor or semiconductor device that can amplify electrical signals as they are transferred through it from input to output terminals".

More technically it's able to manipulate/condition input signals: less technically, think it able to take some - limited - decisions about inputs, when it's properly configured. Configuration is a key word.

Common Emitter is one, and is related to an extreme of BJT; so let's take a brief look to a Bipolar Junction Transistor.
It has three parts, central Base (B) more thin than extreme ones, which are Emitter (E) and Collector (C); names are quite self-explicative and junction zones are just Junctions.

In particular we need to know how to recognize E from C, because they're ideally equal.
Simplifying a complex matter, during BJT building E is strongly enriched with charges while C only weakly, but with charges opposite of B's ones.
What does it means?

We know only electrons (negative charges) are responsible for current's flowing in a metal, and it's the same for semiconductors, with a particularity: their behavior let's us to distinguish two kind of charges:

1. negative; classical electrons;
2. positive; not positrons, but electron's absence or holes (electrons move among "empty spaces", so that we see relative positive charges).

Too much to say: better to stop with boring theory, while it's good to pick the juice up.
If we want E and C with positive charges then we enrich them with elements full of holes, otherwise full of electrons; B will be opposite to E and C, and this gives us the possibility to regulate BJT's behavior.
Bipolar term indicates the capacity of hosting two kind of currents, and simultaneously; indeed what missed from previous talk is that they are all present in BJT but with enrichment (called doping) we make one of them be the most important.

NPN means E with electrons, B with holes, C with electrons; PNP opposite.
Figure shows NPN active, it means that power supplies $V_{BE}$ and $V_{CB}$ let current to externally flow from E to C: pay attention because this is a convention, because for historical reasons current is considered positive, in the sense of positrons; the reality wants electrons flowing from E to C but internally.
Simply if positive current has a direction, negative has opposite.

Lastly, note in picture how E is denoted with a N++ while a C with a N+, remarking the different doping level between them.