Thermodynamic and kinetic control are used to explain what product is formed when a reaction offers different reaction pathways.
Suppose a compound A, which can be converted into either product T (thermodynamic) or a product K (kinetic), and that all reactions are reversible. Product T is always more stable (has lower energy) than product K, but product K is formed faster (has a lower energy of activation). This means that if A is let allowed to react, both products T and K will be formed, but in the beginning of the reaction mainly product K will be formed (because this reaction goes faster).
Now, if you were to stop the reaction after only a short amount of time, product K will be the major product. We then say that the reaction happened under kinetic control (there was no time for the more stable product T to be formed). If, however, the reaction is allowed to run for longer times, then mostly product T will be formed. The reaction is then under thermodynamic control.
Usually, kinetic control means short reaction times and lower temperatures, while thermodynamic control means longer reaction times and higher temperatures (because the energy of activation is higher).
In your case, you should know what defines the stability of double bonds in terms of substituents, their position, and conjugation.
Also, thank you sjb.