Some people think of 'living by faith' as the life of 'servants of God' who do not have a regular income but who expect to receive gifts from others! No. We are all expected to live by faith, because without faith it is impossible to please God (He.11:6). V.5 talks about how Enoch was pleasing to God and we can see how he must have walked by faith.
V.4 tells us how Abel offered a sacrifice by faith. It was this sacrifice by faith that made his offering better than his brother Cain's. Some people explain that it was because Abel offered an animal sacrifice while Cain had only offered the fruit of the ground. We see from the law of Moses that Cain's offering was also an acceptable form of sacrifice to God. What made it unacceptable to God was that it was not given in faith. If Abel had offered an animal sacrifice but not in faith he also would not have been accepted!
Let us try to understand what it means to offer something to God in faith. Faith is our trust in God that comes out of a personal relationship we have with Him. We know Him, we know He can be trusted, we know that what He tells us to do is for our very best, and then what we offer to Him is out of our love for Him, gratitude to Him, etc. It will not be out of a sense of duty that we do it, nor will it be out of fear that He might hit out at us if we didn't. In that kind of a relationship as a child to the Father, it is not the material of the offering that matters, but our motive and attitude as we give it. That seems to be what made the difference between Abel and Cain.
Look at our life to see if we are really living by faith, or only thinking that on a certain day in the past we came to Jesus by faith. Whatever service we give to the church or to His people, whether we give money, use our talents, sing in the choir, help others, pray for others, attend Bible studies, etc., are we doing them from our heart because of our faith in God and love for Him, or merely because they are what we are supposed to do?
Whatever we do, we are to do it from the heart 'as unto the Lord' (Col.3:23). It is when we do things because of our relationship with the Lord and our heart's delight in them, that we are living by faith. If we are not doing things by faith but merely because of religious compulsions, they become 'dead works', and just like Cain's offering, will be unacceptable to God.
Isn't it good to examine our life in this light and look at the different things we do? Next time we stand in a worship service and sing songs with clapping or raised hands, see how much meaningful it is in our heart, or if we are just singing along while our thoughts are somewhere else. I am not thinking about our level of concentration. But if our heart is not in it, can we say it is being offered in faith?
What we can understand from the example of Abel and Cain is that this is how faith makes the difference. Let us try to clear ourselves more and more from dead works.