This is a very intelligent question. Both words come from ancient Greek: chronos means time, dia means through, and syn means with or together. From this breakdown, we can say that a diachronic study deals with the evolution and change of a word over time. We can say that it is basically a historical study of words or languages (historical linguistics).
A synchronic study limits its concern to a particular moment of time. The point here is to study words and lanugages without regard to the historical development of a word or language.
An example will be helpful.
The Greek word hamartano means to miss the mark. So, in classical Greece, when an archer misses the bullseye, he misses the mark. That is what synchronically means.
However, when we come to the Bible, the word harmartano means something different. It means to sin. Over time, the word began to change and took on new meaning. This approach is diachronic.