Peek is a core scouting ability, allowing you to look at a location card without activating it. This can be used to prevent landing on really bad cards, or it can be used to keep from wasting powerful "when flipped" cards.
It benefits from the Hidden status, so it pairs nicely with Hide.
It also works as a reaction. While some reactions - like Block - are made to be used when it is not your turn, Peek benefits from being a reaction in that it basically doubles your chance to draw it; if there's a space that you really need to look at but you don't have a Peek action card, you can end your turn and draw up. If you draw a Peek, you'll be able to Peek before anyone else moves onto that location.
At the beginning of the game, Peek may only be used to look at connecting spaces - adjoining locations that you could move to. However, if you level it up to 10, you can look at any location in range 1, even if it doesn't connect. Since range is counted diagonally, this allows you to look at locations diagonally or separated by walls, doors, etc. This can be very helpful for safely scouting for other members of the party.