A bird base is a square base plus two petal folds. After you've folded your square base, fold the top left and right triangle flaps in to meet the center crease. Unfold. Fold the top of the model down so you have a horizontal crease connecting the creases you've just made. Unfold. Open the upper flap, pressing the sides of the model inwards at the same time. Flatten the paper into a tall, thin diamond shape. (This is very similar to Step 3 of the origami lily model featured in the square base lesson.) Flip the paper over and repeat on the reverse side to finish the bird base form.
The bird base gets its name because it's used to make an origami crane, one of the most famous origami models of all time.
To make an origami crane: