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I'm currently working on PSBT and I try to understand all the part of the original implementation.

Dealing with base64 PSBT encoding: it seems that we convert the buffer from a base 8 to a base 6 using the convertBytes function.

Is someone that could explain me the aim of this conversion ?

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PSBT uses Base64 encoding. As every Base64 character has 64 = 26 possibilities, they can store 6 bits of information. The ConvertBits function you link to takes input bytes (which consist of 8 bits each), and rearranges them into groups of 6 bits, which are then mapped to the Base64 character set.

ConvertBits<A,B> is not converting from base-A to base-B; it is converting from base-2A to base-2B.

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