An extreme point or pole. Geographically it can mean the north or south pole; more generally it denotes a climax, an extreme point, or a mathematical/singular point.
探検隊はついに南極の極点に到達した。
The expedition team finally reached the south polar point.
複素関数の研究で極点の性質を調べる必要がある。
In the study of complex functions, it is necessary to examine the properties of poles.
フェスの熱気は夜には極点に達した。
The festival's excitement reached its peak by night.