Generally when FF is acting up, it's a badly coded extension.
HTML5 (yes, it's written like that - no .0, no space) is a new version of HTML, the language used to write webpages. The plan is to make a natural development of HTML 4.0 (the current version) by standardizing behaviour that has developed over the last decade and adding some new features. The plan is to get away from complicated Javascript libraries and Flash and use standardized code. It is written by WHAT-WG, a group that includes representatives from Mozilla, Opera, Apple and Google, and which was recently joined by a representative from Microsoft. It is currently in the process of releasing working documents for HTML5 and its components RDFa, Microdata and Canvas. That process has recently been held up over an objection from Adobe to the W3C.