Respiratory System
The respiratory system is the organ system that brings oxygen into the body and removes carbon dioxide, mainly through the lungs.
Definition
The respiratory system is the set of body parts that let you breathe: air goes in through your nose or mouth, down your windpipe, and into your lungs, where oxygen enters your blood and carbon dioxide leaves. It consists of the nose, pharynx, larynx, trachea, bronchi, bronchioles, and lungs, plus the diaphragm and rib muscles that move air, and its function is gas exchange, with oxygen diffusing from tiny sacs called alveoli into the blood and carbon dioxide diffusing the other way to be exhaled. Ventilation works by Boyle's law: expanding the thoracic volume lowers intrapulmonary pressure below atmospheric so air flows in. Gas exchange across the alveolar-capillary membrane, less than $1\ \mu\text{m}$ thick, follows Fick's law of diffusion driven by partial pressure gradients; oxygen is carried mainly by hemoglobin, while $CO_2$ travels mostly as bicarbonate formed by carbonic anhydrase in red blood cells. Ventilation rate is set by brainstem centers responding primarily to blood $CO_2$ and pH, not oxygen.
Example
Take a deep breath: your chest expands, air rushes in, and oxygen from that air is in your blood within seconds, headed for your muscles and brain. Inhaled air is about $21$ percent oxygen and $0.04$ percent carbon dioxide, exhaled air about $16$ percent oxygen and $4$ percent carbon dioxide, and human lungs contain roughly $300$ to $500$ million alveoli with a total surface area of about $70\ \text{m}^2$. Alveolar oxygen partial pressure is about $100\ \text{mmHg}$ while venous blood arrives at about $40\ \text{mmHg}$, so oxygen diffuses into the blood, and $CO_2$ moves the other way from about $46$ to $40\ \text{mmHg}$; at rest an adult moves about $6\ \text{L}$ of air per minute, rising to over $100\ \text{L}$ per minute during hard exercise.
Key Insight
You breathe out carbon dioxide, not just "used air," and that carbon dioxide was made inside your cells when they released energy from food. Breathing and cellular respiration are different things: breathing moves gases in and out of the lungs, while cellular respiration is the chemical reaction inside cells that uses the oxygen. The urge to breathe comes from rising $CO_2$, which lowers blood pH, rather than from low oxygen, which is why holding your breath becomes unbearable well before oxygen actually runs short and why hyperventilating before a dive is dangerous.