According to Kant, there are two different dimensions along with judgments can differ.  There is the distinction between a priori and a posteriori judgments and there is the difference between synthetic judgments and analytic judgments.  Synthetic a priori judgments, then, are one possible kind of judgment.

Kant says that some judgments can be made a priori.  That is, they can be made independent of any experiences we might have.  They are logically necessary.  One possible example of this would be the conclusion that “all mothers are female.”  You do, of course, need experience to know the meanings of the words “mother” and “female.”  However, so long as you know the words, you know the statement is true.  You do not need to have experienced any mothers to know the statement is true.  Instead, it is obviously true just by its definition.

Kant also says that some judgments are synthetic.  This means that the conclusions they come to are not necessarily contained in the very definition of the subject.  Kant’s example of a synthetic judgment is the statement that all bodies are heavy.  He says that the idea of heaviness is not necessarily part of the idea of a body.  He says that it is necessarily true that all bodies have dimensions (this is an analytic judgment because the idea of size is inherent in the idea of a body), but it is not necessarily true that they all have heaviness.

Kant holds that there are judgments that are both synthetic and knowable a priori.  For example, the idea that the sum of the internal angles of a triangle is 180 degrees is such a judgment.  Kant says this idea is not inherent in the idea of a triangle, but it is always true and so we do not need to test it out in order to know it.

There is a great deal of controversy as to whether Kant’s distinctions and categorization of judgments is valid.