A question is a move that forces a player to choose between two or more available options in an area of the board. The player can either answer the question, by playing one of the available responses, or not answer and play elsewhere. However, if the original question is sufficiently forcing, it must be answered right away.
Sometimes a player has a choice of accomplishing one of several different things in a given region, such as: choosing to connect one stone vs. another, connecting more strongly vs. denying the opponent a ladder escape, etc. In such situations, it is often in the player's interest to postpone the choice as long as possible, to keep their options open until they know more about what is going on on the rest of the board. By playing a question, the opponent can sometimes force them to make the choice earlier than they would have liked.
Of course, in some very general sense, every move is a question, namely the question: "How will you respond to this move?". But usually the term is applied more narrowly in some region of the board that is not quite settled, where one player plays a move that forces the other player to settle it, or at least significantly simplify it, in one of several ways.
A joseki can be viewed as a sequence of questions and answers.
Perhaps the simplest example of a question is playing in the center of a U-turn. The U-turn is the following position, consisting of two overlapping bridges:
With Blue to move, Red has a choice between connecting A to B or connecting A to C, but Red cannot achieve both of these things simultaneously. By playing in the cell marked "*", Blue asks the question "which or B or C do you want to connect to?"
The following is a position where asking this question is the only winning move for Blue:
With Blue to move, in the upper part, Blue gets to choose whether Red connects B or C to the top edge. In the lower part, Blue can force Red to choose whether to connect B or C to the bottom edge. By playing the question at "*", Blue forces Red to make this choice. If Red chooses B, Blue blocks B on top and vice versa.
Example: Edge template with two stones
Consider the following edge template:
This template has the curious property that, with Blue to move, Red can choose to connect either A or B to the edge, but cannot guarantee to connect them both. (See edge templates V-2g and V-2h).
Blue can ask the question "Which stone to you want to connect?" by playing at either of the cells marked "*". Red does not need to decide right away. For example, in the below diagram, if Blue intrudes at 1 and Red responds at 2, Red still retains the potential to connect either stone. But if Blue then plays at 3, then Blue threatens to cut off A at x or B at y. Red cannot defend both.
Similar, if the game proceeds like in the next diagram, then after move 7, Blue threatens to cut off A at x or B at y, and Red cannot save both connections.
Of course, there are many other lines of play to consider. If Blue is not careful at each move, Red might be able to connect both A and B. But if Blue plays correctly, Red is eventually forced to answer the question.
Example: Obtuse corner
It is relatively common for a player to occupy the fourth stone on the short diagonal:
One way to ask this stone a question is to play e9:
Assuming Red wants to reconnect her stone to the edge, she has two main choices. She can either play at c8, gaining more strength on top, or at c10, gaining more strength on the bottom. (There are also several other moves that would reconnect Red, but they are generally no better than c8 or c10).
If Red plays the minimaxing move at c8, she connects to the edge by edge template IV2a and gaining significant strength toward the top:
In this situation, Red has a 2nd row ladder escape in the corner, and Blue has a potential 2nd row ladder escape fork. However, Blue can decide to take away Red's 2nd row ladder escape at the expense of also giving up Blue's ladder escape, by playing like this:
If Red plays at c10, Red gets less strength towards the top, but gains a 2nd row ladder escape that Blue cannot take away. Blue still gets a 2nd row ladder escape by playing at c9.