Step 1: Henry's law statement.
Henry's law: the solubility (mole fraction $x$) of a gas in a liquid is directly proportional to the partial pressure $p$ of that gas above the liquid: $p = K_H \cdot x$. Higher pressure means more gas dissolves.
Step 2: Explaining Bends.
Deep-sea divers breathe compressed air at high pressure. The elevated partial pressure of $N_2$ forces a large amount of nitrogen to dissolve in blood (Henry's law). If the diver ascends too rapidly, external pressure drops suddenly. The dissolved $N_2$ cannot exit fast enough and forms bubbles in blood vessels and joints, causing severe pain and embolism: the bends (decompression sickness).
Step 3: Explaining Anoxia.
At high altitudes, atmospheric pressure is much lower, so the partial pressure of $O_2$ is reduced. By Henry's law, less oxygen dissolves in the blood, giving insufficient oxygen supply to tissues. This deficiency is called anoxia, causing dizziness and weakness in climbers.
Step 4: Summary.
Bends: increased $N_2$ pressure at depth causes excess $N_2$ dissolution; rapid decompression releases it as bubbles. Anoxia: reduced $O_2$ partial pressure at altitude reduces $O_2$ solubility in blood.