1A wall or partition — the vertical structure that encloses or divides a building or room (interior wall, exterior wall, etc.).
絵を掛けるためにリビングの壁にフックを付けた。
I put a hook on the living-room wall to hang a picture.
隣の部屋との間に薄い壁があるだけだ。
There is only a thin wall between the adjacent rooms.
外壁のひび割れを補修してもらった。
I had the cracks in the exterior wall repaired.
2Figuratively, a barrier or obstacle that hinders progress, as in "言語の壁" (language barrier) or "心の壁" (an emotional wall).
新しい仕事でまず言語の壁を乗り越える必要がある。
In the new job, I first need to overcome the language barrier.
創業には資金という壁が立ちはだかることが多い。
Starting a business is often blocked by the barrier of funding.
二人の間には長い間、心の壁があった。
For a long time there was an emotional wall between the two of them.
3"Wall," one of the 28 lunar mansions in traditional Chinese astronomy, read へき. A specialized term almost never used in modern speech.
古代の星図には壁（へき）という星宿が記されている。
Ancient star charts record a lunar mansion called 'Wall' (heki).