The common collector or grounded collector configuration is generally used where a high impedance input source needs to be connected to a low impedance output load requiring a high current gain.

Why common collector configuration works as a current amplifier?

This circuit is mainly used for amplification because of this arrangement input resistance is high, and output resistance is very low. The voltage gain of the resistance is very low. This circuit arrangement is mainly used for impedance matching.

Why common base configuration is used?

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The common emitter and common collector (emitter follower) configurations are far more widely used because their characteristics are generally more useful. The common base amplifier configuration comes into its own at high frequencies where stability can be an issue.