Vital signs are T, P, R, BP. Temperature, pulse (heart rate), respirations, and blood pressure. These signs are called vital because they must be in certain ranges to sustain life.
Take temperature for example, the normal body temp. is 98.6 F, if the temperature gets too high (febrile) it can have devastating effects on the organism. Or if the temp. is too low (hypothermia), this also is not compatible with life.
Pulse or heart rate must stay within a certain range to adequately perfuse organs with blood. A very low HR will not accomplish this and a very high HR causes many types of damage to the myocardium and other organs.
Respirations and blood pressure are similar insofar as they also must stay in certain ranges to adequately deliver needed oxygen to the cells of the body and perfuse organs. A low BP (hypotension) will not deliver enough blood to the organs and a very high BP (hypertension) has detrimental consequences.
Vital signs are called vital because they are vital for your existence. Without healthy vital signs your life is at risk, and without them at all you are dead. They are essentially the bare minimum required for a person to still be considered living, and an indicator of which direction a person's health is taking a turn for.
The most important vital sign is a pulse. It's actually why in Canada they ammended CPR to exclude breaths, and to contain compressions only. It is absolutely important to get the heart starting again. Once it is pumping your body should (barring internal injuries) begin breathing on its own again.
If the word vital is causing your confusion, here are some synonyms: cardinal, critical, crucial, fundamental, imperative, important, key, life-or-death, necessary, required, significant, and urgent.