The g Factor, or general factor, is a number representing general performance in mental tests of arbitrary test content. It was proposed by Charles Spearman in 1904 after recognizing that children's test performance on unrelated subjects were correlated. wikipedia 
The consistent finding of universally positive correlation matrices of mental test results, despite large differences in tests' contents, has been described as "arguably the most replicated result in all psychology - wikipedia
Multiple Intelligences is a critique of a focus on g Factor as a predictor of success.
The theory of multiple intelligences is a theory of intelligence that differentiates it into specific (primarily sensory) "modalities", rather than seeing intelligence as dominated by a single general ability - wikipedia