inner part; interior; depths; back
Refers to the physically deep or far part of a space: the back of a drawer, the depths of a forest, the end of a road, etc. Also used for the throat or other body parts.
森の奥に小さな神社がある。
There is a small shrine deep in the forest.
引き出しの奥から古い写真が出てきた。
An old photo came out from the back of the drawer.
inner room; living quarters at the back
Specifically the private living area of a traditional Japanese house, located away from the entrance. Often used in the phrase 奥の間.
お客さんを奥の間に通した。
I showed the guest into the inner room.
recesses of the mind; bottom of one's heart; hidden depths
Abstract use: the deep, hidden, or true part of one's mind, heart, or an art. Common in expressions like 心の奥 and 言葉の奥.
彼の言葉の奥には深い悲しみが感じられた。
I could sense deep sadness behind his words.
心の奥では、彼女も同じことを考えていた。
Deep down, she was thinking the same thing.
There is a bookshelf at the back of the room.
We went deeper into the forest.
A voice could be heard from deep inside the house.
I put it away at the back of the drawer.
Deep in my heart, I had been sad the whole time.