The term "vital" is sometimes used as a synonym for "living", and that is what it means in this case. Vital signs are those which are present in a living being, and all need to be within a certain range for life to be sustained. A health assessment, no matter how basic or how intense, will usually start with taking and recording these vital signs: resting pulse rate, blood pressure, temperature, and respiratory rate. All of these are reliable indicators of cardiovascular function and overall metabolic level.
If any of the vital signs is not within normal range, that is an immediate indicator that the body systems are under some sort of strain. If a person was under a physical stress such as exercise, we would expect all of these signs to be high, but we would also expect them to drop to normal when the person stopped exercising. If one or more of them failed to do so, that would be a sign that further examination is required.
Recording the vital signs and keeping them with the patent's chart is a good way to discover subtle changes early on, particularly with cardiovascular health. A reading that is still within the normal range, but that shows a trend, can be an indicator that lifestyle changes are needed to slow or stave off a chronic condition such as hypertension.