The final puzzle in this age is to use the mommy bird for something productive. Down at the bottom level are some giant blue plants. One plant is open. You need to open the second plant too and go inside. Note a fan-plant above which you can use to block the light reaching the big blue plant. Now, back at the base of the blue plant is a little dome plant - when you click on it, it releases spores. The flies should run away. Now that there's no light and no flies, it closes.

So now go to the other plant, use one of those reflecting plants to get light on it, and the flies should be there since you scared them off from the first plant.

Now find the root that leads to the plant, and go inside it. You should be able to get inside the plant, at which point you'll find some levers, and mommy bird will come take you to its nest!

The Myst 3: Exile Walkthrough