RDF or Resource Description Framework is a generic model for describing objects and data. The basic unit of RDF is the triple, which consists of a subject, predicate, and object.
Representations
RDF/XML is a common representation, and unfortunately is intimidating, miserable to work with by hand, and just barely gets by as human unreadable (it's designed for machine consumption).
RDF/N-triples (aka RDF/N3) is a quick-and-easy representation by Tim-Berners Lee. He has a beginner's N3 primer.
Turtle is another natural language-looking, N3-like syntax by Dave Beckett.
RDF/JSON is a description for RDF in JSON, perfect for use in browser-based web applications. Freebase also uses some kind of RDF-in-JSON representation, though different.
Dave Beckett has a summary on various RDF representations in 2010.
RDFa
RDFa is a mechanism for embedding RDF triples in HTML attributes.
Discussion
HTML5/RDFa arguments: why RDFa isn't being included in HTML5
Competing formats
Microformats are oriented around special attribute values that go into elements' class= attributes. It has no support for namesspaces. It is not compatible with RDF.
Microdata is a section of the draft HTML5 specification that adds a set of new attributes (itemprop, etc) to better expose data than microformats. Has some kind of support for namespaces. It can be made compatible with RDF.
Microformats vs RDFa vs Microdata: great article contrasting the three competing formats
