"Transferred from original analogue master tapes"

My take on it is, most important thing to know about buying records is yourself. Are you a sound quality buyer? If so then marketing schtick like original analog master tape is just that, marketing schtick. The luck of the draw in terms of the quality of the individual pressing you happen to get has far more to do with the sound quality you will hear than anything else. Are you a record collector? If so then you will be happy to have what no one else does, the rare original test pressing of, well whatever. The one with the accidentally printed upside down cover, I guess. Are you a fan? Impulse? Buy the hits follow the crowd? 

Whatever it is the more you are honest with yourself the better luck you will have. 

If you are a sound quality buyer there really is only one source for records of guaranteed extreme high sound quality- Better Records. Not cheap, but they are the only records I know with a 100% money back guarantee if you don't like the sound. Which they are able to do because unlike all the others they actually do have the sound quality, original master or no original master. They don't care. Only thing Tom cares about is how good it sounds. 

What it is supposed to mean is they used the original master tapes to cut the LP. But notice this is a compilation.

So, think about it. Records are cut on a cutting lathe. They don’t stop the cutting lathe between tracks to change tapes. This is why Direct to Disc is so rare, the performance has to be real-time continuous. Same goes for cutting from tape. The only way they can use original master tapes on a compilation LP is to first make a copy of the master tape tracks they want to go on the LP.

Then think about how record labels handle their tapes. The original master is the first tape of the mix-down. As such all the tremendous investment of resources is distilled down to that one tape. Studio execs abhor risk, and this is major monster risk. First thing they do is make a copy, at least one, and away goes the master to a vault makes the one in Indiana Jones look all neat and tidy.

Merely finding one of these Ark’s of the Covenant is an archeological epic. Tracking down a slew of them to make a compilation? Dream on!

I could go on. And on.

Bottom line. What does "transferred from original analogue master tapes" mean?

Marketing. That’s what it means.