Why is germanium used in amplifiers?

For the same reason silicon is, they are both semiconductors and thus can be used to make transistors which can be used to build amplifying circuits.

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It isn't any more. Aside from all the other drawbacks to Germanium (more expensive, noisier, less able to handle high voltages), it becomes "intrinsic" at a fairly low temperature. A pure semiconductor material is called intrinsic, it's also called an insulator. If you put the probes of your ohmmeter in a pail of sand - the material all silicon semiconductors start out life as - the meter will sit there and look at you like "now why did you do that?" To make it do its thing you have to "dope" it with boron or arsenic. Once you spice up your silicon (or germanium, in the case of this thread) with dopants, it's called extrinsic material. Well...what happened is Motorola built a bunch of transistorized car radiOS with germanium components back in the 1950s, and when the weather got hot the radiOS all quit working...because at slightly elevated temperatures germanium forgets it's doped.