Cross a threshold is an idiom that means to pass a certain point or boundary, usually figuratively. It can be used to describe a person crossing a physical threshold, such as entering a room, or it can be used to describe a person crossing a metaphorical threshold, such as taking on a new challenge. In this case, the answer to the crossword puzzle is ENTER, which is a verb that means to go into or onto a place. Therefore, the phrase 'cross a threshold' can be interpreted as entering a new place or situation.