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In order to make sense of a geometry_msgs/Pose message, you need to know the reference coordinate system and the intrinsic coordinate system. These should be clear from the context in which the Pose message is used. To specify the reference coordinate system, many ROS packages use the frame_id field of geometry_msgs/PoseStamped instead of using Pose directly.

For example, robot_pose_ekf publishes the robot pose as PoseStamped, where the reference coordinate system (the fixed world frame, if you like) is odom_combined, and the intrinsic coordinate system of the robot is base_link. As the document linked to by @dornhege points out, the default axis orientation for a body (e.g., a robot) is "x forward, y left, z up". So the interpretation of this particular Pose message is "rotate base_link by the rotation given in the quaternion, relative to the odom_combined frame".

More specifically, if I have a orientation (w, x,y,z) in 3d to what orientation this corresponds in 2d?

Generally: none. :-)

Ok, just being cheeky. In cases where a body can only move in 2D (like all the 2D navigation stuff), the rotation axis should be the z axis, so (x, y, z) = (0, 0, 1), since z is "up" (see above).

In order to make sense of a geometry_msgs/Pose message, you need to know the reference coordinate system and the intrinsic coordinate system. These should be clear from the context in which the Pose message is used. To specify the reference coordinate system, many ROS packages use the frame_id field of geometry_msgs/PoseStamped instead of using Pose directly.

For example, robot_pose_ekf publishes the robot pose as PoseStamped, where the reference coordinate system (the fixed world frame, if you like) is odom_combined, and the intrinsic coordinate system of the robot is base_link. As the document linked to by @dornhege points out, the default axis orientation for a body (e.g., a robot) is "x forward, y left, z up". So the interpretation of this particular Pose message is "rotate base_link by the rotation given in the quaternion, relative to the odom_combined frame".

More specifically, if I have a orientation (w, x,y,z) in 3d to what orientation this corresponds in 2d?

Generally: none. :-)

Ok, just being cheeky. In cases where a body can only move in 2D (like all the 2D navigation stuff), the rotation axis should be the z axis, so (x, y, z) since z is "up" (see above). Using the naming conventions from your link, that means that (n_x, n_y, n_z) = (0, 0, 1), since z is "up" (see above).