The term a posteriori is used in philosophy to indicate inductive reasoning. The term is Latin, meaning “from what comes after”, refering to that which comes after experience.
Something that is known a posteriori is known based on logic that is derived from experience. Reason can be involved in an a posteriori statement, but that reason still stems from an assumption made empirically, rather than one derived from an abstract truth.
A posteriori knowledge is often compared to a priori knowledge, which is knowledge that is known to be true based on reason alone.
Compared to a priori knowledge, such as a mathematical equation, a posteriori knowledge is more likely to be false, since it relys on an interpretation of an experience.
Your date of birth is something known a posteriori. You cannot reasonably argue that your date of birth occured on any particular day or time without knowledge that has been acquired empirically — either a record of your birth (such as a birth certificate or dated home video), testimonial from a witness (such as your mother) or some freakish ability to remember your own birth.
Like all a posteriori knowledge, this statement could be false. A posteriori knowledge is often considered to be true, and is often very likely to be true, but it is not infallible. In this example, a number of things could cause this knowledge to be false: birth records could have been misprinted or falsified, a testimony could be a lie or your freakish recollection could be inaccurate or even imaginary.
Other a posteriori knowledge includes things like the orbits of planets, the contents of an atom or the placement of an object in your home. Even things that are observed indirectly through reason, such as black holes (which cannot be seen directly since they do not emit any radiation), are considered a posteriori since the reasoning is based on other empirical data, such as the gravitational effects of a black hole on neighbouring bodies.