Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun The number of arguments or operands taken by a function or operator.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun logic, mathematics, computer science The number of
arguments oroperands afunction oroperation takes. For arelation , the number ofdomains in thecorresponding Cartesian product .
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun the number of arguments that a function can take
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

r is called the arity of the function f, i.e., the number of arguments that it takes.

Then due to its popularity, the dates were extended twice until the end of August.

A structure contains interpretations of certain predicate, function and constant symbols; each predicate or function symbol has a fixed arity.

A signature is a set of individual constants, predicate symbols and function symbols; each of the predicate symbols and function symbols has an arity

In 1870 Peirce published a long paper “Description of a Notation for the Logic of Relatives” in which he introduced for the first time in history, two years before Frege's Begriffschrift a complete syntax for the logic of relations of arbitrary adicity (or: arity).

Then due to its popularity, the dates were extended twice until the end of August.

Again: rheme (by which Peirce meant a relation of arbitrary adicity or arity) was a first, proposition was a second, and argument was a third.

These axioms tacitly specify the arity of a combinator as well as their reduction (or contraction) pattern.

P and Q (or for predicates of higher arity when the variable in their last argument is bound).

Predicates have a fixed finite arity in FOL, and nothing precludes binding at once a variable in the first argument of one predicate and in the second argument of another predicate.
sionnach commented on the word arity
the number of arguments that a predicate takes. Generally, a predicate with arity n is called an nplace predicate. Another term for arity is adicity.
October 14, 2009