To 'know' has two meanings in English: to be aware of facts, or, to have an intimate experience of something or someone. The Greek word used here (the Greek has four meanings!) means 'a knowledge based on personal experience'. Jesus said He has an intimate understanding of those who follow Him. He also said that His 'sheep' interact with Him in a personal way.
 
In any interactive relationship, we know as much of the other person as we can understand; so a mother may 'know' her child better than the child knows its mother. In the same way, Jesus knows us through and through, because He understands everything. The reason Christ died for us was because He knew all the worst about us, but loved us so much that He was willing to be punished for the wrong we do. But perhaps it is surprising to know that Jesus knows us as well as God the Father knowing God the Son. And even more surprising still that one day we shall know God as He knows us (1 Corinthians 13:12).
 
Knowing Christ starts with a personal and intimate encounter when we repent of our sin (all of which He already knows) and receive Him as our Lord and Saviour. After that, although He already knows us completely, we get to know Him better as we understand His Word with the help of the Holy Spirit; discover His answers to our prayers, know Him guiding us, and showing us what He is like, as we interact with Him. It is a wonderful adventure to discover the character of God as we live with Him each day. That adventure will keep on surprising us, and is as real at work as at home or in Church. Getting to know God is the most wonderful experience ever!