"And if a soul sin, and commit any of these things which are forbidden to be done by the commandments of the Lord; though he wist it not, yet is he guilty, and shall bear his iniquity.  And he shall bring a ram without blemish out of the flock, with thy estimation, for a trespass offering, unto the priest: and the priest shall make an atonement for him concerning his ignorance wherein he erred and wist it not, and it shall be forgiven him.  It is a trespass offering: he hath certainly trespassed against the Lord."

Leviticus 5v16-19
In these verses we have a number of interesting items.  The first, is that the Holiness of God is portrayed, then the Grace of God is displayed.
The Holiness of God is seen in these verses in that people can sin without knowing it and is still guilty before God.  This is particularly relevant today, when mankind is convinced of it's own holiness.  God's commands are completely ignored, or when they are taken notice of they are watered down.  "It's not relevant in today's society" is a phrase that I have heard time and again.  People have tried to take God's word and make it more acceptable, but this should not be.  God gave His word, and the Old Testament is there for our learning.  Just because we are Christians does not mean that we should ignore it.  Indeed, we do so at our peril.  It is through the Old Testament books that we see what God is like and what His standards are.  Also, the entire Old Testament looks forward to the coming of His Son (as we shall see in the Grace of God). 
One other comment before I move on.  The Message (a Bible in book form), translates v17 as,

If anyone sins by breaking any of the commandments of GOD which must not be broken, but without being aware of it at the time, the moment he does realize his guilt he is held responsible.

I feel that this needs to be corrected, because the original Hebrew does not allow for the above to be correct.  God did not wait for men to realize that they were incorrect.  The idea is that the man was guilty of the sin whether he knew it or not.  An example of this is found in the story of Job, "And it was so, when the days of their feasting were gone about, that Job sent and sanctified them, and rose up early in the morning, and offered burnt offerings according to the number of them all: for Job said, It may be that my sons have sinned, and cursed God in their hearts.  Thus did Job continually." (Job 1v5).  Bear in mind that Job existed before the commands of Leviticus were given to Moses.  However, we can see that Job continually sacrificed to God not only for himself but for his children as well, just in case they had sinned.  Job did not wait for them to realize their sin, but gave an offering to God first.  Also, look at 1 John 4v10, "Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins."  God did not wait for us to love Him, but because He loved us He gave His Son.
The Grace of God is seen in the provision of a sacrifice for the ignorant sins.  I am sure that if you were asked to list all the sins that you had ever done you would not remember most.  However, God knows every single one.  In this passage God shows us a picture of what He would do through His Son.  As already considered, God did not wait for us to realize that we were guilty, but provided a way for us to come to Him.  The difference is that the Jews were able to give a sacrifice in case they had sinned.  Though the sacrifice has been made, God's Son was sacrificed in place of every sinner, we must accept this gift for it to be of any worth.  It is impossible to say, "I'm ok.  Christ died for me." and then live the life we have always lived.  One person once said to me, "I'll make sure I'm ok just before I die."  The only problem with this is that we do not know when that day will come.  All we are assured of is right this minute, as you sit there reading this.  I do not know if you will survive to the end of this document.  I cannot guarantee one more minute of my life, yet I do not worry because I have accepted Christ as my Saviour.  Indeed, I can say with John, "We love Him, because He first loved us." (1 John 4v19). 
God has provided a Sacrifice for your sins.  Will you be like the Roman soldiers and crucify Him?  Will you sit there and be like the Pharisees, Scribes and Priests who rejected Him from the start?  I challenge you to study the Scriptures and decide for yourself.  Remember though, that by not making that decision you have rejected Him already.