How do I "Push up edge padding"?

I’m making models for my game, and recently I uploaded what I had done on IndieDB.

Somebody pointed out that white lines were showing up all over my characters, where I made seams for the UVs. I’ve also noticed this for a long time, but ignored since it only occurred when I rendered the model in Blender.

Here’s what I’m talking about:

Notice all of the White lines all over the character?
It isn’t as bad now, as they aren’t as many seams (I’m making proper UVs for the characters now), but it’s still noticeable.

I’ve tried everything to get rid of them, painted outside the UV lines, shrinking the UVs, etc.

The user suggested I “push up edge padding”… what do they mean by that? How do I do that? Sorry, I’m still fairly new to Blender.