Does the Jewish day begin at sunset or nightfall? For example does Sabbath begin at sunset or nightfall?

Shalom, Thank you for your question. The Jewish day starts at nightfall, and continues throughout the night and following day, until the next night. This is based on the first verses in the story of creation (in the book of Genesis), where it says "it was night, and it was day – day one [of creation]". The status of the dusk – that is from when the sun sets below the horizon – until it is truly dark (usually measured by the appearance of three medium sized stars in the sky) is a question of debate amongst the early Rabbis. Today we treat this time period as a doubt, and as such we are strict to act as though it is both night and day, whichever side will be strict. For example, on Friday afternoon we start the Jewish Sabbath a few moments before sunset – and treat the dusk period as night, and therefore already Sabbath. But on Saturday night, we do not finish the Sabbath until three stars have appeared in the sky – and thus treat the dusk period as part of the day. I hope this is of some help to you. Blessings.