Practical significance

A hypothesis test tells you whether there is convincing evidence of an effect; practical significance tells you whether anyone should change what they do about it. The size of the effect and the setting decide that, so the same difference can matter enormously in one context and not at all in another. For example, a supplement that lowers average blood pressure by 0.4 mmHg could be statistically significant with 100,000 subjects and still be clinically pointless. A confidence interval helps you judge it, since a narrow interval that excludes zero but sits close to it says the effect is real and small.