I have a theory that I came up with while watching Lost, actually. But I also have a few that I have accumulated over the months I've known about Slenderman. These aren't really about why he does what he does, they more focus on HOW he does it.
The first part is optional, it can be flexible in that the second part of my theory could make this part unnecessary. I've heard this one before, that there is not just one Slender but multiple, even an entire species. Since not everyone sees them all the time, they might be an incredibly small race. We already know they have a knack for being able to hide themselves when they don't want to be seen. In addition to these factors, they might not even naturally reside in our world or dimension. This could explain why there have been no remains of such a creature found, if they leave anything behind at all. Their inhuman behavior could be explained by concluding that they are some sort of supernatural being with the ability to manifest themselves on a physical plane. Think of them as a poltergeist on steroids.
So what is their roll as a species? I'm still thinking about this one. A few thoughts come to mind. Maybe they are a step up from us on the food chain. It's the Slender's natural desire to feed on humans, because to them we are exactly like pigs, cows, and chickens are to us. We've been eating those animals since the time of our ancestors, so it might be the same for the Slender. Except vegetarians and vegans and a handful of other people, most don't take into consideration that they've murdered a living creature for their own survival, because it's been going on for so long that it is okay. The Slender could be the same, in that they have constantly found their meals within our flesh so they do not believe they are doing something wrong. This would attribute to the theory that Slenderman is not an evil, negative being.
My main theory has to do with how the Slender can teleport and seem to be in multiple places at once. What if he can manipulate his position in time? Because we are human, and can only exist in one point in time, we think of time as "past" and "future" with wherever we are as "present." Time is linear to us. However, I don't think of time like this. Time, ANY "time," is continuously happening at any given moment. With this theory, the future has technically already happened, and the past hasn't happened yet. You may be having a hard time understanding, so I'll make an analogy.
Think of a stream. A single stream, flowing through the woods. The water is always flowing one way. There aren't parts where the water suddenly flows against the current (that's a paradox, since the water itself creates the current). Think of the water as time. A leaf falls into the stream, floating on the surface. It floats down the river. The leaf is us humans. Now, the area that the leaf floats on is not the only part of the water that is moving. The ENTIRE stream is always moving, always flowing, always continuing. Just like time. Ancient Egypt is still happening, Hitler is still at large, the dinosaurs are still roaming. But they are different leaves on different parts of the stream, so we consider all those things in the past. The reality is that their leaves just haven't floated down the river as far as we have. In theory, we could pick up our own leaf and drop into the river at any point, essentially dropping ourselves into a different time. This is the always-pondered desire of time travel, which we still haven't achieved. But I believe it is very possible.
Now, we can apply this theory to Slender. If we agree that he is not human, we might agree that he is some sort of supernatural creature. He demonstrates his ability to cause disorientation, sickness, paranoia, visions, unconsciousness, and other mental effects. What if that's not all he can do? My theory is that the Slender has the ability to manipulate his position in time. He can pick up his own leaf and place it wherever he wants. This could be an explanation as to how he teleports. He is not actually teleporting, he just accelerates in the stream of time so he can be in a different location in what seems like a mere blink of an eye.
I hope this isn't too long or crazy, but I kind of started typing and my brain threw up on the computer. XD I do hope you enjoyed hearing my theories. Maybe you can form some of your own from what I've said here. Have a good day, and don't look behind you.