For reference: Loremaster (d20pfsrd.com)
Relevant part to question:
There are secrets for with requirements for each number 1-10.
My question is what level is being referenced in the Secret description, the one telling you which ones you can choose? Is it the Loremaster level or the character level?
It doesn't make a whole lot of sense for it to be the character level, because the entry requirements include 7 ranks in any two Knowledge skills, which restricts you to entering it no earlier than 8th level. That would mean you have 8 + Int at the time of getting the first secret, and as it is directed towards Int-based spellcasters, it's basically a moot point. If it is character level, then there might as well be no requirement period.
Loremaster level makes more sense to me, but I think any time a level aside from character level is referenced, it's usually noted as such.
Loremaster levels are being referred to. Anytime you see a reference to level in a prestige class such as this, unless it is called out otherwise, it is referring to the character's level in the prestige class. So you would get a total of 5 secrets if you took 9 or 10 levels in loremaster, at the class levels indicated (1, 3, 5, 7, 9).