Dialogue - the bit where your characters talk to each other. It's important. It's also kind of hard to do right.
The thing is that dialogue in fiction has to read and sound like real conversation without being like real conversation.
Real conversations are confusing things full of interruptions and elisions that would make a written conversation unreadable. So - as I've said before - you are trying to catch the essence of speech without its confusion.
In practice what this means is there are two common mistakes authors make with dialogue.
1. They make it too formal. The character's say things no one would - which removes transparency of writing. Not a good thing.
2. They try and making it authentic and fill it with pauses, interruptions, repetitions, missing bits, slang and dialect to the point it is unreadable.
The best way to get round this is to read it aloud - if it sounds stilted it's probably got problem 1. If it's impossible for a single person too read it aloud it's probably got problem 2. Try to write dialogue that is both comprehensible and sounds natural when read aloud.
Once you know what's wrong with it you can start to fix it. It's one of those things you just have to keep plugging away at until you get it right. I still get it wrong sometimes (probably a lot of the time).
And now the useful links on the subject: