The difference between direct and indirect characterization is the same as the difference between telling and showing. One is simply the the author telling the reader what the character is like. The other is where the author shows the character in action, and the reader gets to realise for themselves what the character is like.
So an example of the direct characterization might be:
Peter was very lazy, and would never shift himself more than was absolutely necessary.
The same information, as indirect characterization, might be something like:
Peter was bored with the TV programme, but the remote control was inexplicably across the room, so he just watched it anyway. Jan'd be in soon, and she could fetch the remote control for him then.
It's good discipline to try to use indirect characterization as much as possible as that draws a vivid picture in the reader's mind (which is what you are always, always aiming for). There are times, however, to use direct characterization (e.g. for a minor character, or to portray a minor trait), and it's part of your judgement as a writer as to when you're going to use that.
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