Storage unlocks at a Journal score of 300. If you have a bird you no longer want in your forest, or want to make more room for new species, you can put birds into Storage!
To access the "Storage" area and see the bird inventory, simply tap the button along the bottom toolbar which looks like 3 birds on branches. Here you will be able to see all birds in your forest and storage areas by selecting from the two tabs. You can move birds between the forest and storage here. From the forest tab to store a bird, tap on a bird then select "store" and the game will tell you that you can choose multiple birds to move. You can then either select more birds before you proceed or you can just continue on with 1 bird, and select the "Confirm" button. The game will ask if you are sure and you will need to confirm. To return birds from storage to forest the process works similarly, only you use the "Return" button. Please note you will need to have enough room in your forest to return birds.
You can also Store birds directly from the forest by locating the bird, tapping on it and then selecting the "Store" button.