Why is understanding the context so important when it comes to interpreting the Bible? Because it is very easy to think the Bible is saying something that is completely alien to what the original author had in mind. Here is a short but sweet video (less than 4 minutes) by Alan Shlemon at Stand to Reason ministries that helps to explain context.
Here are the Bible verses that Alan is talking about from John 14: John 14:16 and John 14:26. For more detail regarding why Muslims see Muhammad as being predicted by the Bible, look here. Interpreting the Bible is all about understanding the basic concepts of hermeneutics, which is a fancy word that simply refers to the study of the interpretation of texts.
If you are not sure what the big deal is regarding context, see this earlier Veracity post on Taking the Bible “Literally.”