John 3:16 has to be the most often quoted and memorized Bible verse. Tim Tebow wore it on his eye black. That guy used to hold up a sign that just said, John 3:16, in the football stands under the goal posts. You just know what John 3:16 says even if you haven't spent a lot of time in church.
But what does it mean? That's another question altogether. Does God love the whole world, like everybody? How did He give us His Son and how does that work anyway? What is His great purpose for all of us? Long chapters of theology have been written on each of those questions. A very popular series of books by a very popular West Coast pastor mined the riches of that last question (The Purpose Driven Life).
Perhaps we have made it more complicated than it is. Eugene Peterson says that verse contains everything we need to know about God, and all of it is good. Frederick Dale Bruner in his commentary on John calls this verse the heart of the gospel and the international treasure.
I have preached on this verse many times but I think, not enough, and were I to do it over, I would preach on it and it's themes more.
Here they are: First, is the world-wideness of God's love (Bruner's term). God so loved the whole, entire ball of wax (the cosmos), all of us, each one of us. His love should not exclude any group or any one.
Second, God loved the whole world, as is. With all it's waywardness, failures, flaws and fallenness (sin) and He gave for, one and all, His only Son, Jesus Christ. We celebrate his death and resurrection for us at Easter, and every Sunday and every day when we arise. There are many theories of how this works, of how Jesus's death saves us from our sins, and you can study them for a long time but, essentially, they all say what John says here. That is, that God's giving was historical and local and personal - in Jesus Christ. And that God gave personally (his own self), and that his love is not just a feeling but an action that cost God and benefited us. (Bruner says, consider that event and bow your head in wonder!)
Third, ..."so that every one, every single person, who is believing, entrusting him or her self to God... We have a hard time with the simpleness of this statement. We would clarify it with adverbs like totally, or wholly, or sincerely where the gospel has no qualifiers at all. It says it simply, simple trust is all that is needed. Our salvation depends on God our Savior not on us. Bruner again, we do nothing but trust Another who has done everything. Trusting is like breathing - it is ongoing, continually resting in the divine love (Bruner).
Fourth, the direction of our trust is "into Him". John's teaching on belief is not just "belief that"; it is that AND a personal commitment to.
Fifth, such simple trust brings Life not merely life. (John's gospel fleshes out all of these themes).
We (my wife and I) sang Love Divine, All Loves Excelling from the hymnbook and it's a good thing our only audience was God!