A seal's oxygen store is not in its lungs. It carries a blood volume proportionally far larger than a human's, with high haemoglobin concentration, plus muscle myoglobin at concentrations high enough to make the tissue almost black. The spleen holds a reserve of oxygenated red cells and contracts during a dive to release them. 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. Seals therefore exhale before descending and their alveoli collapse progressively, driving remaining air into reinforced airways where gas exchange cannot occur.
During the dive, heart rate falls dramatically and blood is shunted away from the gut, kidneys and skin to protect the brain and heart. This dive response is present in a 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 tags reach animals that were never testable in a laboratory.