The definition you're getting from your dictionary reflects one contemporary usage of the word subjectivity. But the word has had many meanings. The most basic meaning is "that which inheres in a subject".
A long time ago (scholastic medieval period), this would mean following Aristotle, that which is true of a substance in itself -- without being accreted to the thing. During that period, objective means what subjective means to us and vice versa. Kierkegaard is not referring to that usage, however, so let's set it aside.
To understand what Kierkegaard is doing, we need some knowledge of Danish Hegelianism (which may or may not be that good of an interpretation of Hegel). Danish Hegelianism was in vogue in Kierkegaard's time. The basic claim was that everything can be comprehended, i.e. that objective reason and understanding is the pinnacle of thought.
One of the other answers rightly refers to Socrates' influence on Kierkegaard's philosophy here. Kierkegaard here is echoing the Socratic notion found in the "Crito" of know yourself. For Kierkegaard, the point of the claim truth is subjectivity is that anything that is true is true for a subject. In other words and in particular, if the Christian story is true, then it changes everything for the subject in a way that cannot be overlooked or erased.
Contrary to that answer, I wouldn't go so far as to say "Kierkegaard does not believe in 'objective truths.'" Instead, I would say Kierkegaard thinks it matters only secondarily whether something is objectively true, because what matters is that the subject accepts that it is true by living accordingly.
To give an example, if I believe that I can fly, then this should impact my behavior. If it doesn't, but I say "objectively speaking I can fly", then who cares.