'tis a riddle most excellent. 
-djh
My guess is Leveling.
You don't, actually 
You don't, actually
Please my friend, tell me more.
It takes the settings that the user has control over form the Rig that you pick. So that's all the Amp Block settings, all the stomps, reverb, delay, sense settings and so on. Those all get left as is, which means during profiling it doesn't modify the sag, definition, compression, clarity etc settings, just a bunch of internal settings that you don't have access to.
It also gives you the rig as a comparison at the beginning when you're doing leveling, so you want something that sounds vaguely similar when setting up your gain setting, EQ at that point (though honestly I tend to leave that all at <0.0>.
So basically if you're going to go through the amp block, the EQ etc and change it all at a later point then it's not important, but if those settings matter on a particular profile you're going to want to pick that profile as a starting point.
Which brings up an interesting question. For these settings, does the Kemper compensate so that e.g. you set up the EQ to match your amp's settings at the beginning, make your profile, will it then compensate against the EQ so that the sound profiled matches the real amp's sound when the EQ (or other amp) settings are where you set them, or does it simple apply them so you only get the true profiled sound when the stack settings are all at <0.0> regardless of where the settings where beforehand?
Because if that's the case then it would make sense for the profiler to rest all the stack settings to their defaults during profiling so you can comparing doesn't get thrown out by the changed settings. If however it compensates for the settings then that's also important as it means that having e.g. a high definition or clarity setting at the start will mean you can only really reduce clarity or definition (and conversely a low setting would only allow you to raise those values).
I'd really like to know more about exactly what happens in this scenario.
Per,
Are you saying that every profiled amp that has a non-default setting anywhere (Clarity, Tube Bias, or etc.) is the result of inheriting that setting from the 'reference' amp you started with and/or post-profile user tweaking? I expect the profiled EQ's to register as flat, but... the rest?
That seems so wrong, it injects another variable into the mix (the other being the 'refinement' process.) This could be a new use for the "CK Initialized" profile...
-djh
I'm saying that this is stuff I want to know too!
I'm pretty sure the EQ etc stuff is just applied to the two signals, so the Amp block is simply swapped out signal wise for the input from the real amp during profiling doing A/B, that way the real amp gets the EQ and everything else (but the cab) applied to it's signal too to enable comparison using the A/B switch.
But, the Amp block settings seem to be inherited from the profile you were last using before entering Profiling mode, which is why I'm curious as to how that's handled.
It takes the settings that the user has control over form the Rig that you pick. So that's all the Amp Block settings, all the stomps, reverb, delay, sense settings and so on. Those all get left as is, which means during profiling it doesn't modify the sag, definition, compression, clarity etc settings, just a bunch of internal settings that you don't have access to.
Oh, it definitely adjusts the definition. No pun intended. I would think the whole amp/cab blocks are reset but I can't recall.
It takes the settings that the user has control over form the Rig that you pick. So that's all the Amp Block settings, all the stomps, reverb, delay, sense settings and so on. Those all get left as is, which means during profiling it doesn't modify the sag, definition, compression, clarity etc settings, just a bunch of internal settings that you don't have access to.
sorry, that's just not right.
rig settings, as Stomps and Effects will be part of the resulting rig, that's correct.
the profile, which resides in the Stack section, is entirely created by the profiling process and parameters as Compressor, Clarity, Pick, Direct Mix etc are initialized while Definition and Power Sagging are determined by the profiling.
The Definition setting of the profile you used as a starting point has no impact on the new profile.
The best reason I can think of to choose a similar profile as a starting point is that you could probably keep a few tags with minimal edits. 
'Nuff said
