Many corneal defects are not easily seen with direct illumination. Such things as microcystic edema, microcysts, and neovascularization are examples.
Retro-illumination is where a relatively narrow beam (1-3 mm) of light is reflected off the iris and the object of interest is viewed against the bright iris. If the object is opaque it will appear dark in retro.
Indirect is similar except you view the area of the cornea next to where the light beam is hitting the cornea and not against the reflection from the iris. In practice both are used more or less simultaneously.