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My broad and beginner answer: The first stage is a "class A" amplifier that provide some voltage gain. This gain is proportional to the transistor beta. The second stage is an emitter follower and it is basically just boosting the current: it's voltage gain is about 1, but it allow you to drive the load of the speaker without affecting the first stage. The emitter follower also known as common collector, has a large output impedence about \$\beta * R_l\$ and a low output impedence.