I recently wrote 2000 words on the word 'and' in an essay for a Pragmatics course at UCL. Whilst this sounds impressive and slightly bewildering, some academics have spent a lot longer puzzling over this little word, generating books, articles and decades of work.
Pragmatics looks at the gap between the linguistic meaning of what people say and the actual meaning of their utterance. These are rarely the same thing, as meaning is invariably partly derived from context. (A simple example: 'I love you' expresses something different depending on who you are and who you're saying it to).
'And' causes problems because sentences like 'John fell out of a tree and broke his leg' seems to imply that the falling happened before the leg breaking, and that the former caused the second. The question is whether these extra meanings come from the word 'and' itself, or are pragmatically derived.
The answer isn't simple, or even agreed upon. Robyn Carston, incidentally also my lecturer, gives an account within The pragmatics of sentential coordination with and, which is in turn based upon Relevance Theory, proposed by Dan Sperber and Dierdre Wilson.