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Design Patterns are a way of describing recurring problems and their solutions in a language-neutral way, focussing on how the problem presents itself and how to solve it. The best site that I've seen to explain patterns is the Portland Pattern Repository at http://c2.com/ppr/. You will not regret spending an hour browsing it. The "Pattern Language Catalog" is more strategic and the "People, Projects, & Patterns" is more tactical but both are worth the investment in time.

BNF Grammar - BNF grammars are used for describing things like programming language syntax and message formats. Here's a brief introduction: http://www.garshol.priv.no/download/text/bnf.html