This is never explained in any writings.
If I had to speculate, there are a few possible reasons I could think of:
The Great Goblin is a maiar spirit. In a late essay, Tolkien discussed the possibility that some of Morgoth's Orcish lieutenants were maiar in the forms of Orcs. If this was the case, the Great Goblin could have seen the swords personally.
This seems unlikely, however, for a few reasons:
- We would expect the Great Goblin to be rather more impressive if he were a maiar spirit (though, after so long in a single form, perhaps not)
- The quote suggests that all of the goblins recognized the blades, and they can't all have been maiar
Some kind of passed-down history. Glamdring and Orcrist are clearly central to the goblin's history, so it's not beyond imagining that stories about them, or depictions of them, would have been passed down.
On his blog, Michael Martinez presents a possible out-of-universe explanation:
[I]t could be that this part of the story represents an unedited holdover from the original placement of the tale in the “Elder Days”. The goblins would not have to have been quite so ancient in order to be familiar with Biter and Beater
The claim that The Hobbit was originally set in the Elder Days is supported by referencing John Ratleiff's The History of the Hobbit, and I cannot personally confirm it; but Martinez is pretty trustworthy, so I'm inclined to take him at his word.
