g is that which is common to (shared by) all tests for mental ability, and is the largest source of variance in test scores. Typically, 60 to 70 % of test score variance is accounted for by g. The rest consists of group factors (shared by some - at least three - but not all tests), specificity (unique to one particular test), and measurement error. Examples of group factors are verbal, numerical, and spatial factors.
g is an empirical phenomenon that has been discovered by Charles Spearman (1863-1945). It is inferred from the intercorrelations of mental ability tests. It is an empirical fact, not a theory, and is well defined, and not controversial. A priori there is no reason whatsoever why g should exist; it just happens to be so that all tests for mental abilities intercorrelate positively. Although many use the word "intelligence" in relation to mental testing, g is the proper scientific term to use, "intelligence" being too ambiguous, ill-defined, and controversial.
g is the largest source of intraspecies variance in mental ability within Homo sapiens; that is, responsible for most of the individual and group differences in mental ability among humans.