Why is it easier to tear paper along a crease?
To word it differently: why does a "tear" progress along a crease, if one is present?
Paper is made from wood, and wood is made from long fibers.
Typically the manufacturing process leaves the fibers are more or less parallel. So it is easier to tear in the direction that separates fibers from neighboring fibers than in the direction that breaks fibers. Wood is the same. It is easier to split a log than chop it.
Creasing paper breaks and/or separates some of the fibers, making it easier to break/separate the rest.
Once the tear is started, pulling the paper apart a little propagates the tip of the tear a little farther. The crease makes the paper fail more easily along the crease. So the tear follows the crease.
By folding a piece of paper you deform the paper there locally. I am not sure if you can call this plastic (instead of elastic) deformation, like with metals. At least with metals it is the case that plastic deformation leads weak spots, such that when a uniform tension is applied the material will tear first at these spots.
I am not an expert on how paper gets damaged when folded. But I expect it will not act much different. It might not behave the same in all direction since it is made up of fibers, which it its direction of orientation.
Once the paper has a tear it will lead to stress concentrations. Therefore it is more likely that the tear will grow instead of new tears forming.
By the way when I want to tear a piece of paper along a straight line, I often fold the paper in both directions and before tearing I make the crease wet (with some saliva) which makes the crease an even bigger weak spot. I am not exactly sure though why paper is easier to tear when wet.