If it has anything to do with molecular gastronomy, it's only incidental. A "gastro pub" is a "pub" which promotes itself as a good restaurant in addition to being a pub. It's a matter of emphasis. Many pubs have food -- most often of the general type called "pub grub." Usually a "gastro pub" has higher goals, or at least higher pretensions. Not always though.
By the way, a "pub" isn't necessarily the same thing as a "bar," although there's a lot of overlap. A pub usually has a public room, a lounge and (often) a restaurant. Although, sometimes the functions of any two, or all three are combined. Since we're using the English language, and talking about traditions in constant flux we're going to run into a lot ambiguity. Neither the ideas nor the words are very precise.
If it helps, a gastro-pub has more in common with the restaurant and bar of an inn, than with a simple bar -- even one which serves food.