From Webster's New World Dictionary, Third College Edition:

soffit n. 1 The horizontal underside of an eave, cornice, etc.

 

Thanks Aaron. I too looked it up - I also googled it and checked the encyclopedia. According to Webster's definition, my rain damage is on the soffit. But I've also heard this term used to describe the entire enclosure created in/by the part of the roof that extends horizontally beyond the wall. So, in that case, the whole overhanging section is the soffit. Also, I've had a couple contractors refer to the "damaged eaves" not soffit, when looking at the rain damage on my house. I've also heard the stud and drywall enclosures sometimes built around HVAC ducts (like in finished basements) referred to as "soffits" - which would support the idea that a soffit is (or can be) an enclosure. Thus my confusion...

Argh.

 

I believe I call the Eave is the part where the fascia meets the roofline (where the roof edge goes). The soffit is everything underneath the fascia to the wall.