Most LSAT books tend to define "sufficient" by using the word "necessary," and then define the word "necessary" by using the word "sufficient." This is shitty teaching, plain and simple, because a student would never be able to understand one term without already understanding the other term. Don't worry, this concept is a lot easier than you might think. It's really just common sense. This is the first concept I teach to every class, and it's very simple. I need my head to live. My head is necessary to live. If I don't have my head, you know that I can not live. That's what "necessary" means.
If you see me come into the classroom and teach a four-hour LSAT class, then you know that I am alive--you have "sufficient information" to know that I must be alive. Seeing me teach a class is sufficient, i.e. enough, to know that I am alive. That's what "sufficient" means.
The LSAT will frequently confuse a necessary condition for a sufficient condition. Like this: "Nathan has his head, therefore we know he is alive." Uh, no. Nathan could very well be dead will still having a head. (As a matter of fact, he would strongly prefer to die that way.) Having a head is necessary for life, but it is not sufficient.
The LSAT will also frequently confuse a sufficient condition for a necessary condition. Like this: "Nathan wasn't in class tonight, therefore he must be dead." Uh, no. Nathan could be on the golf course somewhere, or he could be in a drunken stupor. Or, ideally, both! Being in LSAT class is sufficient for life, but it is not necessary.
I swear to God, that is all there is to the whole sufficient vs. necessary thing. It's easy, and it's the most commonly-tested flaw on the entire LSAT. Many students will pick up 5-10 points just by understanding this one simple concept.