a place of asylum: a city set apart to take in and shelter someone who has killed another person by accident
This word is used in only one setting in the whole Bible: the cities of refuge. After the land was divided, six towns were marked out so that a person who killed someone unintentionally could run there and be safe from the dead person's family, who had the right and duty to avenge the killing. The refuge was not a free pass. The killer had to stand trial, and if the death really was an accident, the refuge city became his protected home until the death of the high priest, when he could finally return to his own land.
The root behind the word carries the idea of taking someone in or receiving them, so a refuge city is best understood as a place that absorbs the fugitive and holds him, rather than simply a hiding spot. That is why the same towns can feel both protective and confining: they shelter the innocent from hot-blooded revenge while keeping a person responsible for a death within bounds until the matter is settled.
The word always appears with or near the word for "city," naming an institution more than a feeling. It is the asylum town itself, the safe place the law provided so that the wrong person would not be killed in the heat of grief.