You are a walking biological weapon, try to sterilize yourself and your clothes as much as possible first, and quarantine yourself until any novel (to the 13th century) viruses are gone. Try to avoid getting smallpox and any other prevalent ancient disease you're not immune to.
Have you tried flying into a third world nation today and dragging them out of backwardness and poverty? What would make it easier in the 13th century?
If you can get past those hurdles the obvious benefits are mathematics (Arabic numerals, algebra, calculus) and standardized measures (bonus points if you can reconstruct the metric system fairly accurately), optics, physics, chemistry, metallurgy, electricity, and biology. For physics specifically the ability to do statics for construction and ballistics for cannons and thermodynamics for engines and other machines (and lubrication and hydraulics are important too). High carbon steel for machine tools, the assembly line and interchangeable parts. Steel reinforced concrete would be nice, but not a necessity. Rubber. High quality glass for optics; necessary for microscopes for biology to progress past "We don't believe tiny organisms make us sick". The scientific method (probably goes without saying) to keep things moving instead of turning back into alchemy and bloodletting.
Electricity and magnetism eventually; batteries won't cut it for industrial scale use of electricity (electrolysis, lighting for longer working hours, arc furnaces for better smelting) so building workable generators that can be connected to steam engines is vital.
Other people have mentioned medicine, which is pretty important from an ethical perspective, but difficult to reverse centuries of bad practice. Basic antibiotics and sterilization is probably the best you'd be able to do, but without the pharmaceutical industry there's a lot of stuff you can't do. If you know how to make ether, at least get anesthesia started.
"Have you tried flying into a third world nation today and dragging them out of backwardness and poverty? What would make it easier in the 13th century?"
I think this is an interesting angle. How comparable are 'backward' nations today with historical nations? Obvious differences in terms of technology existing in modern third world even if the infrastructure/skills to create and maintain it don't. In that way, I suppose they're more comparable to places in the very early middle ages, when people used Roman buildings etc. that they coudn't create themselves. But I also wonder how 13th century government compares to modern governments that we'd consider 'failed states'.
Imagine that you were instantly transported into (roughly) the 13th century. I'm not great at history, but I'm picturing sometime around the crusades. You're sitting there, reading this post on your computer, and BAM! Some guy in chain mail is asking you if thou art the spawn of a demon.
Given this situation, I present to you a challenge:
You are stranded in the past. You have no modern technology except your everyday clothes. The only thing you do have is your knowledge from the future.
What do you do?
I'll make this a little more structured for the sake of clarity.
1) You appear in Great Britain (or the appropriate analogue for your native culture).
2) Assume the language barrier is surmountable - in other words, it may not be easy, but you can communicate effectively (by learning the language, or simply adapting to an older version of your native tongue).
3) Further assume that you manage to gain the ear of a ruling lord (how is not important, just say you're a wizard or something) and that he provides you with enough money, labor, and expertise (carpenters, smiths, etc.) to build something *so long as you can describe it in enough detail*.
4) You are only allowed to pull from general, scientifically literate knowledge - high school/bachelor's level only.
5) You can't use your knowledge of future events to your advantage, as it requires too expert a grasp of history. Only your knowledge of the way the world actually works is available.
The reason for 4) has to do with the point of the question. I'm trying to figure out the kind of maps that we have today that are considered "general knowledge" - the kinds of things that are so obvious to us we tend to not realize that people in the past didn't know them.
I'll go first.
The germ theory of disease didn't achieve widespread acceptance until the 19th century. In other words, I'm the only person in the past who is quite confident about how diseases are spread. This means that I can offer practical advice about sanitation when dealing with injuries and plagues. I can make sure that people wash their hands before cutting other people up, and after dealing with corpses. I can make sure that cutting instruments are sanitized (they did have alcohol) before use. And so on. This should reduce the number of deaths from disease in the kingdom, and prove my worth to the king.
I'm trying to build a list of things like this - maps of the way the world really is that we take for granted.
Have fun!