Doge is an internet meme, whose use is rapidly expanding throughout the internet. It is a particular style of language that consists of phrases made up of two mismatched words more often than not, such as very guitar, much delicious, or so paint. These phrases appear next to pictures and photos, usually of fluffy Shiba Inu dogs.
Linguist Gretchen McCulloch spoke on the phenomenon on this morning's Today programme on Radio 4 (listen here for another week - scroll through to 1:43:17). She said that Doge (usually pronounced to rhyme with 'rogue', or like the Venetian dignitary, but also occasionally pronounced to rhyme with 'yoga' or with the 'do re' of 'do, re, mi, fa, so ...') has its own rule-based grammar, even though it's not standard English grammar. The idea is to combine words that don't usually go together, so, whereas very is usually followed by an adjective (very happy, very good etc) in Doge, it is deliberately paired with another part of speech eg very candle or very art. Similarly, other words are paired with parts of speech in a way that is impermissible in standard English eg much happy, such east.
For lots more on Doge, see this article.