​​Why is there a Tiny Hole on your Eyelid?

This diagram pretty much explains it. The holes (the lacrimal puncta, singular punctum) are drainage channels for the tears. As you can see, the tears start at the outer edge of each eye, sweep across it, then drain away into special channels in the nose. Incidentally, this is why your nose runs when you cry. The extra volume of tears is too much for the normal processes to deal with and so the excess spills over.