There are different types of transistor available in the market, but for sake of understanding, we will consider a common emitter mode of NPN transistor. For this let us recall the basic structural features of npn bipolar junction transistor. Its emitter region is heavily doped and wider hence the number of free electrons (majority carriers) is large here.
The collector region is also wider but it is moderately doped hence the number of free electrons is not as much as the emitter region. The base region is diffused in between the wider emitter and collector region but the base region is quite thin compared to the outer emitter and collector region and also it is very lightly doped so the number of holes (majority carriers) is quite small here. 
Now, we connect one battery in between emitter and collector. The emitter terminal of the transistor is connected to the negative terminal of the battery. Hence the emitter-base junction becomes forward biased, and base-collector junction becomes reverse biased. 
In this condition, no current will flow through the device. Before going to the actual operation of the device let us recall the constructional and doping details of an NPN transistor. Here the emitter region is wider and very heavily doped. Hence the concentration of majority carriers (free electrons) in this region of the transistor is very high.
The base region, on the other hand, is very thin it is in the range of few micrometers whereas emitter and collector region are in the range of millimeter. The doping of the middle p-type layer is very low, and as a result, there is a very tiny number of holes present in this region. The collector region is wider as we already told and doping here is a moderate and hence moderate number of free electrons present in this region.
The entire voltage applied between emitter and collector is dropped at two places. One is at the forward barrier potential across the emitter-base junction and this is about 0.7 volt in case of silicon made transistors. The rest portion of the applied voltage is dropped as a reverse barrier across the base-collector junction.
Whatever may be the voltage across the device the forward barrier potential across emitter-base junction always remains 0.7 volts and the rest of the source voltage is dropped across the base-collector junction as reverse barrier potential.
That means none of the collector voltage can overcome the forward barrier potential. Hence ideally none of the free electrons in the emitter region can cross the forward barrier potential and can come to the base region. As a result of the transistor will behave as an off switch.
NB: – As at this condition the transistor does not conduct any current ideally, there will be no voltage drop at the external resistance hence entire source voltage (V) will drop across the junctions as shown in the figure above.
Now let us see what happens if we apply a positive voltage at the base terminal of the device. In this situation, the base-emitter junction gets forward voltage individually and certainly, it can overcome the forward potential barrier and hence the majority carriers, i.e., free electrons in the emitter region will cross the junction and come in the base region where they get very few numbers of holes to recombine.
But due to the electric field across the junction, the free electrons migrating from emitter region get kinetic energy. The base region is so thin that the free electrons coming from emitter do not get sufficient time to recombine and hence cross the reverse biased depletion region and ultimately come to the collector zone. As there is a reverse barrier present across the base-collector junction, it will not obstruct the flow of free electrons from the base to the collector as the free electrons in the base region are minority carriers.
In this way, electrons flow from emitter to collector and hence collector to emitter current starts flowing. As there are few holes present in the base region some of the electrons coming from emitter region will recombine with these holes and contribute base current. This base current is quite smaller than collector to emitter current.
As some of the entire electrons migrating from emitter region contribute base current, rest major portion of them contribute current through the collector region. The current through emitter is called emitter current, the current through the collector is called collector current and the tiny current flowing through the base terminal is called base current. Hence here emitter current is the sum of base current and collector current.
Now let us increase the applied base voltage. In this situation due to the increased forward voltage across emitter-base junction proportionately more free electrons will come from the emitter region to the base region with more kinetic energy. This causes a proportionate increase of collector current. In this way, by controlling a small base signal, we can control quite a large collector signal. This is the basic working principle of a transistor.
