Experiential knowledge of god

In John 17:3 Jesus prayed for us and said: "And this is the way to have eternal life—by knowing you, the only true God, and Jesus Christ, the one you sent to earth!" 

The statement references experiential knowledge. Intimate knowledge. We are meant to have a very real, very personal, fully experiential, actual relationship with our creator. 

From Bill Mounce:
"If ever there were a word that cried out for a word study, it is “to know.” Jesus says, “I am the good shepherd. I know (γινώσκω) my own and they know (γινώσκουσίν) me, just as the Father knows (γινώσκει) me and I know (γινώσκω) the Father”

If these two verses aren’t enough, then John 17:3 cements the deal: “This is  eternal life, that they know (γινώσκωσιν) you, the only true God, and Jesus Christ whom you sent.”

γινώσκω functions as the key term describing not only our relationship with the Son and the Father, but the Son with the Father and the Father with the Son. In addition, it shows there is a correlation between how we “know” the Father/Son and how the Son/Father know each other.
Please stop for a moment and reflect on that. It is overwhelming.

BDAG defines γινώσκω this way. “This verb is variously nuanced in contexts relating to familiarity acquired through experience or association with person or thing.” The important point to note is that it is a knowing that is relational and growing. It is not some fact we accept, but the kind of knowledge that is gained through experience and, if the context allows it, through intimacy.