Mosiah 5

1 And now, it came to pass that when king Benjamin had thus spoken to his people, he sent among them, desiring to know of his people if they believed the words which he had spoken unto them. 
2 And they all cried with one voice, saying: Yea, we believe all the words which thou hast spoken unto us; and also, we know of their surety and truth, because of the Spirit of the Lord Omnipotent, which has wrought a mighty change in us, or in our hearts, that we have no more disposition to do evil, but to do good continually. 
I love this. Not only do they believe king Benjamin's words, they believe ALL of them. Not only do they just believe his words, they know with surety that they are true. This complete shift, from the king wondering if they would believe at all, to their complete confidence came because of the Spirit. This is important because I think we too often operate on the idea that if we could study and understand enough we'd be more confident and secure in our conversion to Christ. Of course study is a part of the process -- but that's not how the actual "mighty change" operates. It's not that we change, it's that our hearts are changed. It is our changed heart that changes us because it changes our "disposition" i.e. "the predominant or prevailing tendency of one's spirits; natural mental and emotional outlook or mood" For example, in the next verse:

3 And we, ourselves, also, through the infinite goodness of God, and the manifestations of his Spirit, have great views of that which is to come; and were it expedient, we could prophesy of all things.
4 And it is the faith which we have had on the things which our king has spoken unto us that has brought us to this great knowledge, whereby we do rejoice with such exceedingly great joy.
Through the spirit our views of the future change -- we become more optimistic and have a positive outlook on things. We see good in people and things and when bad happens, we can see the bigger picture in the context of our faith and trust in the Lord's purpose. Trust in the gospel plan changes our hearts and allows us to know that we have great reason in this life, no matter what, to be joyful. This blessed understanding is what ultimately puts us in a position to choose to covenant with God. Just like king Benjamin's people:

5 And we are willing to enter into a covenant with our God to do his will, and to be obedient to his commandments in all things that he shall command us, all the remainder of our days, that we may not bring upon ourselves a never-ending torment, as has been spoken by the angel, that we may not drink out of the cup of the wrath of God. 
6 And now, these are the words which king Benjamin desired of them; and therefore he said unto them: Ye have spoken the words that I desired; and the covenant which ye have made is a righteous covenant. 7 And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons
and his daughters. 
This is how we become Christians and this is how we are made free:

8 And under this head ye are made free, and there is no other head whereby ye can be made free. There is no other name given whereby salvation cometh; therefore, I would that ye should take upon you the name of Christ, all you that have entered into the covenant with God that ye should be obedient unto the end of your lives. 
9 And it shall come to pass that whosoever doeth this shall be found at the right hand of God, for he shall know the name by which he is called; for he shall be called by the name of Christ. 
What does it mean to be called by the name of Christ and made free? Well in one way, I think it means that we are free from our crummy dispositions. We're all fallen, and therefor our natural-man inclinations are often towards the base and negative. Humanity hasn't changed it's ways in thousands of years and anyone who has tried to change something about themselves will report that it isn't easy (broken new year's resolutions anyone?) True change of ourselves is difficult without a change of our nature -- and that change is impossible without Christ. It is the Spirit which will make "a mighty change in us, or in our hearts" and the Spirit comes when we show God that we are generally interested in trying to find the truth because He has promised that will respond ("And I say unto you, Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you" Luke 11:9). When we learn and live the gospel, the divinity of it is manifest in our lives through the Spirit and we are changed.