1 John 5:13
John tells us in this verse the entire purpose of his epistle 'that you may know that ye have eternal life', read it prayerfully and you will find you answer to "What does it mean to believe?"

Being born again is a supernatural thing, it is not some sort of calvinistic or arminian mental ascension.

If you can live satisfied in sin, you do not believe, if you believed in Christ you would be obedient to what He has taught. He loves you and His commands will not lead you astray. When you live in sin it proves your disbelief, because you regard not what He has taught.

Eternal security rests in the fact that you cannot change your nature. When rebirth supernaturally occurs, and your obedience gives evidence of that belief. God will sustain your obedience. Obedience is natural to you because you were born again, the old man is passed away behold all things are made new.

Just as without an act of grace you were stuck in disobedience (free will or not) with the new nature you are held in the obedient life and the only thing could remove you from that is Christ forsaking you, which He has promised not to do.