A seal's oxygen store is not in its lungs. It carries a blood volume proportionally far larger than a human's, high haemoglobin, and muscle myoglobin at concentrations high enough to make the tissue almost black. The spleen holds a reserve of oxygenated red cells, released by contraction during a dive. Weddell seals routinely dive twenty minutes or more, with some dives well beyond an hour.
Air in the lungs at depth would be a liability, because nitrogen forced into solution under pressure causes decompression sickness on ascent. True seals therefore exhale before descending and their alveoli collapse progressively, driving remaining air into reinforced airways where gas exchange cannot occur. Eared seals, the fur seals and sea lions, do the opposite and dive on a full breath.
During the dive, heart rate falls dramatically and blood is shunted away from the gut, kidneys and skin to protect the brain and heart. The response is present in weaker form in humans, which is why cold-water immersion of the face slows the heart. The upper limits of the physiology are still being revised as tagging reaches animals never testable in a laboratory.