Mark each sentence True or False:
__ "Where are my shoes?"
__ "Beware the Jabberwock, my son!"
Seems inappropriate to call any of these true or false, right? What about this:
__ "He is the tallest man in town."
Out of context, neither answer would fit. If we knew who "he" is and which town we're talking about, then we'd have an assertion which is either true or false (even if we don't know which), in other words: a proposition. Example propositions:
__ "There were more cows than horses in the United States on November 1, 2010."
__ "Gold is an element."
__ "Mental states are fully determined by brain states."
Think of propositions as declarations that something is the case (or is not the case). Or think of them as statements of fact as opposed to emotional expressions, advice, questions, commands, etc. There's a fair amount of controversy about what exactly counts as a proposition, but this is the general idea.