Once I've got a plot, I usually think to myself "What sort of characters do I need for this to work?" and, once I've got an end-game in mind, I think "How do they get there?" and the how is, for me, the gaps in my story, in-between the major events and plot twists that I started with.
As a random example, if I want a character who will ultimately kill the protagonist, I might design someone who is perhaps very goal-oriented; someone who is focused on the ends and can justify murder if they believe it serves a high purpose, be that a virtuous one or their own ambitions. Then I'd have a think about WHY they're goal-oriented, or why they'd want to kill the protagonist - are they close, or do they hate each other? What has made them so goal-oriented in the first place? Depending on what the plot is, I'll use fleshing the character out for the gaps in the story, so things flow and, hopefully, they're a little more connected and a bit more personal for both the characters and the reader - I want the reader to react to the events, but I want them to feel something for my characters as well.
Just an example...probably a poorly explained one, but there we go. xD