The term a priori is used in philosophy to indicate deductive reasoning. The term is Latin, meaning “from what comes before”, refering to that which comes before experience.
Something that is known a priori can safely be considered to be a true statement, assuming that the logic (or deductive reasoning) used to arrive at that conclusion is conducted using valid arguments.
A priori is in contrast to a posteriori, which is a term used to indicate inductive reasoning. In short, something known a priori is known purely through reason while something known a posteriori is determined through empirical evidence.
Although one might venture to guess that something backed up by evidence is more likely to be based in truth, it is often the a priori knowledge that is more likely to hold truth. This is because evidence can often support multiple conclusions and is dependant on our accurate interpretation.
A priori knowledge comes from reason alone and not from experience. Mathematical equations, for example, are an example of a priori knowledge, since they do not require any real-world evidence to be considered true.
(You might argue that all knowledge is based in real-world experience. For example, even math takes root in an original human experience that assigned names to numbers and numbers to orders of objects. Although the knowledge of maths and counting originally sprung from experience, the ideas themselves are abstract. Experience was neccessary to found and test most aspect of reason, but with the tools of reason it is not neccessary to involve experience at this point. That is not to say that experience does not often validate reason.)
So, a simple example of an a priori truth is that 40 plus 5 is equal to 45. This information is known without direct experience; You can calculate the problem as an abstract without needing to arrange forty-five objects and count them.
In the same way, any abstract concepts can be used to arrive at a priori truth. The phrase “all chickens are birds” is also an a priori truth. By knowing the definitions of the word lsquo;chicken’ (ignoring any slang definitions, the word ‘chicken’ itself means a type of bird) and the word ‘bird’, one can use reason to determine that the statement “all chickens are birds” is true without the need to look at any actual chickens.
However, a statement like “my cell phone is in my pocket” is not known through reason alone. You can't be certain your cell phone is in fact in your pocket through reason alone, you must have evidence to support that statement—whether you saw the phone in your pocket or put it there yourself. And as such, this type of a posteriori knowledge can be flawed. You may have put your phone in your pocket and believe the statement to be true, but also be unaware that a thief stole your phone, or that it has been replaced by your friend's similar phone, and that you are incorrect.
It's much easier to believe that a posteriori knowledge is false ("Actually, your phone was taken by a pickpocket.") than it is to believe that a priori knowledge is false ("Actually, 40 plus 5 is 6382.").