How do oil based paints ad depth to painting?

There are different forms of the word depth. The context in which you are describing refers to the paint quality. Oil as a vehicle/binder for pigment adds a luscious and translucent characteristic. Pigment color appears much more rich and retains this richness once it has dried. There is far less color shift as it dries than found with other vehicle/binders of acrylic, watercolor or gouache. Oil is ideal for blending, both, color and edges. The value range is greater thus extending the ability to depict the illusion of three-dimensional depth on a two-dimensional surface.How do oil based paints ad depth to painting?
The paint does not add depth. Depth is achieved by how you use the paint - we as artists are creating the illusion of 3-D on a 2-D surface. There are several factors to get depth - perspective, color (brighter warm color close, neutralized cool color further back), value, shape sizes (bigger closer, smaller as things recede), etc. Hope that helps. There are classes or books in which to study this in more detail.How do oil based paints ad depth to painting?
Sometimes the artist can choose to raise some parts of the painting by thickening the paint so when its dry, that portion looks raised.