For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. - Jn 3:16
And he rejoiced along with his entire household that he had believed in God. - Acts 16:34a
Nevertheless, many even of the authorities believed in him, but for fear of the Pharisees they did not confess it, so that they would not be put out of the synagogue - John 12:42
You believe that God is one; you do well. Even the demons believe—and shudder! - James 2:19
Much - and quite rightly so - is made of the topic of belief - in Jesus, in God, etc. Our salvation depends on believing. But what exactly does it mean "to believe" [in Jesus/God]? And how does one know that their "belief" is "saving belief?" Some, as in the authorities above, believed. The demons believe. And even more curiously, some believe -
Now when he was in Jerusalem at the Passover Feast, many believed in his name when they saw the signs that he was doing. But Jesus on his part did not entrust himself to them - John 2:22f
but apparently Jesus does not believe everyone's "belief."
Clearly, some who "believe" have salvation, yet others who "believe" do not.
So what, biblically, constitutes [saving or salvific] belief and what doesn't?
What does it mean "to believe?" 
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