In this case it means that you were trained by someone who was trained by someone who was trained...Etc by the house's founder.
I always think of it a bit like a magical equivalent of the apolistic succession
The most adulterated True Lineage is House Bonisagus, because they can take apprentices from other magi, even apprentices who have been trained for 14 years in the culture and magic of some other House.
How dare you call us Diedne? We are magi of House Bonisagus engaged in bleeding edge research into the secrets of spontaneous magic....
The gifted members of House Mercere are blood related and all descended from the founder.
But they are the exception and this is the main reason for the low number of gifted Houde members.
Also all descendents of Mercere are pretty much required by the house to have loads of children.
I will make an excuse of faulty memory but isn't there a line that says that Boni snatched apprentices still must server 15 year apprentice with their new master so they are trained with the Bonisagus way? I could have swore I read it somewhere. Of course Players never do this.
The line I remember is that 15 years is the appropriate time for an apprenticeship. I have no recollection of a discussion on integration into House Bonisagus. I also don't recall seeing anything that requires an apprentice who has been elevated to a Bonisagus apprenticeship to join that elite and august house.
Although this asks for clarification on apprentices who do not want to join the rarefied levels of House Bonisagus and yet are not fully trained in their origin house.
I'll have to dig into Apprentices again. It's probably in there.
I am pretty sure not, that would be a serious incentive for Bonisangus to snatch almost ready aprentices rather than find their own. You have a lot better lab assistants that way. The aprentice is pretty hosed to, he is already looking for a longevity ritual by the time he leaves gauntlet.
Seeing how Bonisangus do gauntlet, it doesn't make sense to go to long either. You pass when you show your skill in Magic Theory is great enough. You grabbed an aprentice in his 13th year, and if he needed another 15 years to learn enough Magic Theory, what kind of teacher are you anyway?
The 15 years seem to me that it may be longer but in some cases the apprentice can appeal to a Guernicus to take gauntlet if his master do not make him pass it. So the bonisagus can take an apprentice at whatever moment, but may not enjoy him for fully 15 years, but the apprentice may be apprentice for more time than the normal 15 years.
I think it's discussed in a book... maybe HOH TL, guernicus section?
From the virtue& flaw section we can conclude also that if after 15 years you are gauntleted poorly you probably will have "poor parens" and if gauntleted with more than what is expected, "skilled parens".
But this is certainly not the "true" answer to the "true" question the OP asked .
My guess is that Boni-snatchers snatch only when the apprentice has not been indoctrinated into the ways of their House. It's unlikely that Bjornaer get Boni-snatched after the Ritual of Twelve years.
The idea behind Boni-snatching is to create interesting stories. You have an apprentice? Well, rumor has it, Snatcher filius of McSnatcherton doctrinae Bonisagi is interested in your apprentice... What do you do? Or you play Snatcher, and want another's apprentice...
My guess is the exact opposite: The apprentice becomes a lot more interesting once he has some exotic magic. If you were a Bonisagus interested in a source of Insight for some breakthrough involving shapeshifting or essential nature, wouldn't you prefer the apprentice with a Heartbeast? If you wanted lab help involving Ignem, isn't the Flambeau apprentice with a bunch of Ignem-related virtues better? If you wanted to understand spontaneous magic....
But it becomes more difficult to indoctrinate someone into the House, you illustrate the possibility of taking an apprentice to further some magic, which I suppose is possible, but it would also be a good example of an apprentice who gets killed int he course of the research. Accidents happen...
According to the House, not the Order is how HoH:MC states it.
Or even who doesn't get killed. A newly-Gauntleted Bonisagus might readily see the advantages of belonging to a prestigious House and enjoying its privileges while possibly retaining a connection to his old House. Sort of like a dual-national, or a hyphenated-American with ties to the old country who can wax nostalgic and even visit but (thankfully) doesn't have to live there. Or even drink the Bonisagus Kool-Aid and be more Bonisagus-than-thou.
And of course, there might be Bonisagi who snatch apprentices for purely altruistic reasons, perhaps when he feels an apprentice is being mistreated or insufficiently taught or just unhappy.