We have decided to write about something cheerful, so here is three topics at once: humour, fun, and laughter. They all may be somewhat mysterious and hard to define, though Wikipedia does that.
Humour
There are various kinds of humour, and various theories of humour, but it seems to be more or less common in them that unexpected stuff is funny. And it also is a coping mechanism, providing you relief. One of the oldest theories states that humour is about feeling superiority: you laugh when you see that somebody is acting stupid or suffers; this theory seems to cover most of the funny things, though it may also depend on personal taste. Also explains why snuff got mixed with comedies.
Fun
As Wikipedia states, fun is an experience, related to enjoyment of pleasure, whereas pleasure may be a lot of things, and often it is something you seek. In many cases it is also easy to link to evolution: one usually finds enjoyable the things that helped previous generations to survive. So, basically it is supposed to be fun to survive and prosper.
Laughter
One of the versions of the cause of death of Chrysippus (the guy from the picture, a Greek Stoic philosopher) is that he died from laughter. So, one use of laughter is to send something really funny by mail, following the Unabomber – just using different technologies. Actually, it seems that he does exactly that now, from the prison: “On May 24, 2012, Kaczynski submitted his current information to the Harvard University alumni association. He listed his eight life sentences as awards, his current occupation as prisoner.”
Seriously though, laughter is mostly a social thing, usually caused by humour or other positive emotions, such as joy. Points out that a group of laughing people understands something in the same way, probably is relaxed (hence friendly), and so on.
Smile appears to be related to laughter, though it is not the same thing.
Note that the interpretation of those differs among cultures: say, websites filled with fake smiles seem to be considered appealing in the webdev culture – especially in its corporate and Indian parts, while in sad ex-USSR countries smiling in public is considered suspicious for obvious reasons: you don’t know what to expect from a person who smiles while being in there. Some of the Asian folks may smile when they are in emotional pain, making it pretty weird.