34Hearing that Jesus had silenced the Sadducees, the Pharisees got together. 35One of them, an expert in the law, tested him with this question: 36"Teacher, which is the greatest commandment in the Law?" 37Jesus replied: " 'Love the Lord your God with all your heart and with all your soul and with all your mind.'b]"> 38This is the first and greatest commandment. 39And the second is like it: 'Love your neighbor as yourself.' 40All the Law and the Prophets hang on these two commandments."
Of course, this is an answer that Jesus gave to a Pharisee question, and they are not always as obvious as they appear. But, it seems straightforward enough that I hope you are willing to take it at face value. So, if you accept that our greatest commandment is to love God, one might think it reasonable to ask what this means.
Since I am a fan of Jesus' teachings, I think it is worthwhile to point out that in John's words Jesus says, "15"If you love me, you will obey what I command." in chapter 22. This also seems fairly self explanitory. However, I feel it worth pointing out that Jesus is not ordering us to obey him, or saying that he wants our obedience, but rather that he wants our love, and a natural outgrowth of that love should be our attention to his words, after all, he grants us the same courtesy, when earlier in that same chapter he states, "14You may ask me for anything in my name, and I will do it."
This is a nice simple answer to what the greatest commandment asks of us, but I make no claim to authority in my understanding of the subject. Since the Bible has been around for so long, many longer and more in depth answers have been formulated. I encourage you to search them out, or ask someone trained in this subject, if you want a more detailed answer to the question. And, as always, I encourage you to consider the question for yourself.