noun
Only when written 羽目
Refers to wooden paneling or wainscoting, especially in traditional Japanese architecture. This sense is restricted to the kanji form 羽目.
古い旅館の廊下には、美しい羽目が張られていた。
The hallway of the old inn was fitted with beautiful wainscoting.
noun
plight; fix
Used almost exclusively in the idiomatic expression 羽目になる (to end up in a difficult or awkward situation). Also appears in 羽目に陥る and similar phrases. Not used as a standalone noun for 'situation'.
See also: 羽目になる
うっかり秘密を話してしまい、大変な羽目になった。
I carelessly spilled the secret and ended up in a terrible fix.
彼のせいで、私たちはこんな羽目に陥った。
Because of him, we've gotten into this mess.
窮地 is a more formal, literary term for a predicament or crisis, while 羽目 is colloquial and almost always part of the set phrase 羽目になる.
Originally referred to wooden panels (羽目) used in construction. The idiomatic sense likely developed from the idea of being 'boxed in' or 'cornered' like being enclosed by panels, though the exact derivation is uncertain.