I need help in understanding the above state diagram.
I'm struggling with writing the truth table for this state diagram for jk flip flops
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The state transition diagram (STD) from your post is simply outlining the possible states, the outputs for each state and the transition conditions possible between the states.
In the posted STD, there are 4 states, S0, S1, S2 and S3. That means the system can be in any of state S0 to S3 but not more than one at one time. For each state in the diagram, you can see a bar, with the state name on top and the output on the bottom. So, for all states except S3, the output of the system will be a 0 while in S3, the system will output a 1. That means that as long as you are in that state, the output of the system will be that value. (See Moore Machine: http://en.wikipedia.org/wiki/Moore_machine)
Another important thing to know is how we get between states. Thats what the arrows tell us. Starting in S0 (I assume we start there though there is no explicit entry point from your post), we can either go to S1 (arrow to the right) or stay in S0 (loop arrow) depending on the inputs. The inputs in this case being buttons X and Y. I will also assume like WeSt that the order is {X,Y} so 10 means X is pressed (1) and Y is unpressed (0). So looking at the transitions from S0, we see the loopback arrow has only input 00 while the right arrow to S1 has all the rest listed. That means that if the buttons X and Y are both unpressed (00), we will remain in state S0 (take the self loop) but if either X or Y or both are pressed (01,10,11), we will take the right arrow and go to S1. The rest of the arrows behave the same way, with the arrow indicating a possible transition and the values next to that arrow indicating the conditions under which you take that arrow. (Commas in STD are usually interpreted as logic OR).
Hope that helps you understand the STD! Implementing it is a whole other topic, this site might help with that: http://www.ee.usyd.edu.au/tutorials/digital_tutorial/part3/t-diag.htm