What is an ophthalmologist looking at/for when he puts a lens on the patient's eye after numbing it and looking through a slit lamp?

Retina or angle: A diagnostic contact lens sometimes is used during an eye exam. Sometimes only an anesthetic is used, and sometimes a thicker gel is placed on the lens before going on the eye. A gonioscopy lens looks at the part of the eye where the fluid drains (the chamber angle). This is to rule out risk for certain types of glaucoma. A retinal lens can be used to get an extra sharp 3d view of the retina.

Your eye drain: He/she is performing gonioscopy. He/she is looking at the drainage angle of the eye with this special lens.