What does vital function monitoring actually mean?

For that purpose, the definition of The Cleveland Clinic gives a comprehensible overview.
“Vital signs are used to measure the body's basic functions.

These measurements are taken to help assess the general physical health of a person, give clues to possible diseases, and show progress toward recovery. The normal ranges for a person's vital signs vary with age, weight, gender, and overall health. There are four main vital signs: body temperature, blood pressure, pulse (heart rate), and breathing rate.”
(source: http://my.clevelandclinic.org/health/diagnostics/hic_Vital_Signs)