What is contingent in a contingency table? The Merriam-Webster dictionary defines a contingent event or situation as
1 : likely but not certain to happen : possible
2 : not logically necessary; especially : empirical
3 a : happening by chance or unforeseen causes
  b : subject to chance or unseen effects : unpredictable
  c : intended for use in circumstances not completely foreseen
4 : dependent on or conditioned by something else
5 : not necessitated : determined by free choice

Regarding current statistical terminology, since contingency tables are used to represent a large variety of data in many different situations, why do we call them "contingency" tables? In which of the five senses above is the word "contingency" used in this terminology?
 A: Wikipedia claims that the term was introduced by Pearson in On the theory of contingency and its relation to association and normal correlation. Pearson does indeed seem to have coined the term. He says (referring to two-way tables):

I term any measure of the total deviation of the classification from
  independent probability a measure of its contingency. Clearly the
  greater the contingency, the greater must be the amount of association
  or of correlation between the two attributes, for such association or
  correlation is solely a measure from another standpoint of the degree
  of deviation from independence of occurrence.

(Pearson, On the Theory of Contingency and Its Relation to Association and Normal Correlation, 1904, pp. 5-6.)
Pearson explains in the introduction that he and others had previously considered categorical variables as ordered in all circumstances, and had analysed them as such. For example, in order to analyse eye colour, 

one arranged eye colours in what appeared to correspond to varying
  amounts of orange pigment [...]

The point of the paper is to develop methods for analysing categorical variables without putting some artificial ordering on the categories.
The first use of the term contingency table appears on page 34 of the same paper: 

This result enables us to start from the mathematical theory of
  independent probability as developed in the elementary textbookss, and
  build up from it a generalized theory of association, or, as I term
  it, contingency. We reach the notion of a pure contingency table, in
  which the order of the sub-groups is of no importance whatever.

Thus, contingency is supposed to mean "non-independence". The word contingency is used because two events are contingent if the outcome of one is contingent upon - i.e. dependent upon - i.e. not independent of - the outcome of the other.
In other words, it's related to definition 4 from this Merriam-Webster page.
