What is the term for a white flattened tendinous expansion that serves mainly to connect a muscle with the skeletal components it moves?

The answer is Aponeurosis.

Its a flat sheet of ribbon of tendonlike material that anchors a muscle or connects it with the part that the muscle moves. The aponeurosis is composed of dense fibrous connective tissue containing fibroblasts and bundles of collageneous fibres in ordered arrays. Aponeuroses are structurally similar to tendons and ligaments.