Natural selection isn't something that's applied to individual animals, it's something that exerts pressure on whole populations over many generations.
To go with your Arctic tern example, just because one bird can dive deeper doesn't guarantee it's survival. It might still get eaten by a predator or catch a disease or just have a run of bad luck that causes it to starve. However, the birds that can't dive as deeply run the same risks (assuming there's no additional risk to diving deeply) and, over a long time and with a large population of birds, those that can dive deeper will survive to breed more often, until eventually the whole population carries that trait.
To go with your Arctic tern example, just because one bird can dive deeper doesn't guarantee it's survival. It might still get eaten by a predator or catch a disease or just have a run of bad luck that causes it to starve. However, the birds that can't dive as deeply run the same risks (assuming there's no additional risk to diving deeply) and, over a long time and with a large population of birds, those that can dive deeper will survive to breed more often, until eventually the whole population carries that trait.