Problem in 3D printing of an empty model
You have modeled your bird. So far so good, but you likely only modeled a single surface and not a closed surface body. The crucial step was forgotten, as your pictures 1 and 2 show: you have designed a single surface for most of the object, not a body. To turn the bird into a printable object needs it not to be a single surface but a surface enclosing a volume that has some thickness.

At the moment, it looks like this: 640 vertices, NO enclosed space.



To achieve an even thickness object in blender:


A to choose the whole model
E for extrude Region
Z Z to constrain movement to Z axis
type in the wanted thickness


remember, that the grid in Blender is usually in cm, while slicing programs reference in mm!

close the edges by creating faces there (chose 3 and F)

A to grab everything
W then R to remove doubles, increase the merging distance to 0.05 (it takes away hundreds of superfluous, slightly shifted vertices!)
CTRL+N to recalculate normals

Make sure to check the slicer, because we have some strays, visible in red... where are those? They are faces hidden in the body!



Hide the underside (Select nothing, allow viewing through the object, 3 > B > draw a box around the lowest layer > H)

If you have the normals visible, you'll see the iffy areas now. Fix them by removing the superfluous faces and flipping those that are not superfuous but just inside out (W>F). One example area I highlight in the next picture


In the end, it should look like this in cura:



Make sure to check layer view and possibly thicken some areas manually - or make a box-part for the top, so you can ensure printability. As you'll see, at some scales, some walls are too thin due to how we extruded along Z only.



Alternate ways

As noted in the comments, instead of the Z-Extrude, a model with very vertical walls could benefit from using the solidify modifier. You will have to add it via object mode, modifiers and then choosing solidify and setting a positive thickness. To properly convert the visible modifier into an actual change of the model for the export, you will have to Apply the modifier.

Afterwards, go back to hunting stray internal surfaces and flipped faces.