The reason is because -ck would most likely pick up on your question and answer it. Considering most pools are using the software that he and Kano wrote or custom software based on it, that would have been the best place to ask.
You want the details, here you go:
From Kano's pool help pageA Bitcoin miner creates a Bitcoin block header of 80 bytes, using the work it is given e.g. by a pool, and hashes it using the SHA256 hash algorithm.
Within those 80 bytes, there is a 4 byte value called the nonce - that it cycles from 0 to approximately 4 billion and hashes it for each nonce value.
The SHA256 hash algorithm gives a pseudo-random result for each hash done.
If a hash results in a Difficulty value greater than or equal to the limit specified by the work it was given, it will return the information required to produce the same 80 byte block header it hashed.
A Difficulty value of 1 is expected to occur, on average, once every approximately 4 billion hashes attempted.
If the hash result has a Difficulty value greater than the Bitcoin network Difficulty, then that means the miner found a Bitcoin block!
The bold line is your Share Difficulty. In short, Best Share is the highest difficulty share you have submitted so far. In your case the best is 43,859,517,958.53396 or roughly 44G
FYI, even when solo mining to your own node vs a pool, Shares do have meaning as the node will be constantly sending new work aka shares, to the miner.