If you want a plain and simple explanation, think about it this way:
You know how at school, the computers that are available to students usually have a ton of restrictions on them? You can't install new software, you can't change system settings, sometimes you can't even change the desktop wallpaper. This is because these machines are configured with a very specific and very limited set of privileges, or user permissions. The same thing exists on your iPhone. The iPhone user is barred from making any serious changes to the phone's file system, because they do not have permission to write (e.g. modify file data) within the vast majority of the file tree. Jailbreaking gives you full write access, so you can modify, add, delete, rename, move, etc any file on your phone.
By itself, jailbreaking poses zero risk whatsoever. The reason JBing has an often negative association among some people, is because they either don't understand it and are regurgitating what they've heard from others, they blame the JB for user error, or they installed a ton of crap/pirated apps/outdated tweaks/incompatible tweaks/etc without doing the research first, and think the inevitable slowdown on their phones is a result of jailbreaking. Another reason is because app piracy requires jailbreaking, and many people JB solely for that reason; hence, people associate jailbreaking with stealing apps.
In short, jailbreaking is for the person who wants to feel like they totally "own" their iDevice. It allows the user to enable often very basic functionality that Apple leaves out or ignores. It can make your phone safer than it would be at stock, because whereas Apple can take weeks to push out a software update to fix a security hole, JB devs usually do the same within hours or days (Comex, for instance, released the fixes for the flaw that his jailbreaks exploited).
As long as you do the research, there's no risk. Literally, none. You can always restore and go back to the way it was. Good luck.