coordinate frame (reference frame)
A coordinate frame is a chosen starting point plus a set of directions that you measure everything against. Picture standing in the corner of a room: pick that corner as your zero point (the origin), then call one wall 'forward', another wall 'left', and straight up 'up'. Now you can describe any spot in the room with three numbers — how far forward, how far left, how far up. Those numbers only make sense because you agreed on that corner and those three directions first. That agreed-upon corner-plus-directions is the coordinate frame.
Robots care about frames because a robot is never just one thing in one place. The room has a frame, the robot's base has a frame, its gripper has a frame, the camera has a frame, and a coffee cup on the table has a frame. The exact same coffee cup has different numbers in each one — close to the camera, far from the base, slightly to the left of the gripper. None of these numbers is 'the real' position; each is the truth as told from one frame. Saying 'the cup is at (0.3, 0.1, 0.0)' is meaningless until you say which frame those numbers are measured in.
Because of this, almost every spatial calculation in robotics is really a conversation between frames: knowing where something is in one frame and figuring out where it is in another. Get the frame wrong and a robot will reach a foot to the side of the cup with perfect confidence. So robotics people are almost fussy about always naming the frame, the same way a careful cook always names the units — '200', of what? grams? millilitres? The frame is the 'of what' for position and direction.
A navigation log reads: 'obstacle at (2.0, 0.0, 0.0) in the robot's base frame.' That means two metres straight ahead of the robot — even as the robot turns and drives, the obstacle's world position stays put while its numbers in the base frame change, because the base frame moves with the robot.
The same obstacle, described from the base frame instead of the world frame.
Robotics almost always uses right-handed frames, where if your right hand's fingers curl from the first axis to the second, your thumb points along the third.