‘Both’ is a popular word – in fact, it's a bit too popular. In text like ‘they were both born in the same town’ the ‘both’ is unnecessary, and you don't need it every time two things are mentioned, either. ‘Both’ is at its most effective when it emphasises contrasting elements: ‘She was both strident and sensitive to others.’ Note the ‘and’ in this sentence. Often you'll hear ‘both ... but’, but ‘and’ is correct with ‘both’.
When you see ‘both’, do what I call the copyeditor’s count. In this case, look for two elements. I’ve seen ‘both’ applied to three or more items, and I’ve heard it, in the media, applied to just one.