A priori, a posteriori

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Most generally

A priori roughly means something like "(from) that which goes before".

Often used in a "prior to experience/measurement".

A posteriori roughly means "(from) that which comes after".

Often meaning after experience, often using said experience

A bit more practically

Statistics

In probability and statistics, particularly (statistical) inference, a priori is the prior knowledge of a population.

Basically, it is anything we consider already known, that we can use to improve our model, that is more than just estimations or limited recent measurements. (verify)

A priori probability http://en.wikipedia.org/wiki/A_priori_probability

Posterior probability http://en.wikipedia.org/wiki/Posterior_probability

Also in statistics, the prior probability typically refers to the probability distribution before some evidence is taken into account.

Modelling

In machine learning and pattern recognition, and the models and math that backs it, a priori refers to examples that make for supervised learning (examples that are implicitly taken to be factual/good/positive).

(and a posteriori often short for 'a posteriori estimation' based on it)

Without such a priori examples, the patterns would depend on data behaviour, clustering and such. (verify)

Knowledge (philosophically)

While 'a priori' in the general sense can be translated as 'pre-existing', once you start saying 'a priori knowledge' you put yourself into an epistemological corner with a bit of metaphysics for flavour - i.e. bringing in questions like 'what can we know', and 'what is there?'.

So philosophy's answers try to be a little wider, say, what could be known answers rather than what a person currently knows answers.

A priori knowledge: are things that can be knowable independently of experience/evidence (pedantry: ...aside from the experience of the language to communicate it).

say, anything that follows from logic alone.

e.g. we can say "all bachelors are unmarried" without observing all bachelors. Whereas for other things we need observation.

A posteriori knowledge are things that can only be knowable/verifiable via empirical evidence.

that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.

The distinction is related to objective versus subjective observation,(verify) but not directly.

Law

In law, a priori refers to being based on hypothesis or deduction, rather than experimentation.

It can still refer to subjective, semantic details: testimonials are automatically subject to a priori plausability - personal back knowledge. (verify)