Refers to the time of day around sunset, when it is getting dark. Can be used as a noun or adverbially.
At twilight, the streetlights came on all at once.
This park becomes quiet when dusk falls.
Compound of 日暮れ (higure, 'sunset, nightfall') + 時 (toki, 'time'). The reading ひぐれどき is a rendaku form of とき.