- -ig is an adjective suffix, meaning -y or equivalent.
- ge- is a kind of verbal past tense thing, I believe, so this is an adjective formed from a verb
But then I got stuck (it also turns out I was wrong about the ge- bit anyway).
Just from the way it sounded, I suggested 'cosy', even though it didn't seem right in context. I looked it up when I got home and 'cosy' is one of the things it can mean, but the internet also tells me that this is an 'untranslatable' word.
Untranslatable words, it seems to me, come in two or three flavours. There's one kind where a language happens to have a word for a very specific concept. This is not untranslatable; it's just that language X encodes something in one single word that language Y does with a phrase. See, for example, German schadenfreude or Japanese origami (I have no idea how much Germans or Japanese people actually use these words). In this case, as with many others, the way we get round not having a word for this concept is to just borrow it. We also do this with foreign things like food (risotto, wasabi, pak choi, tea...).
There's also words where the translation isn't exact, although there's a bunch of words with similar meanings. See the Language Log entry on 'accountability', for instance. Prepositions are also a problem - they never seem to translate quite right from one language to another, partly because they don't have 'meaning', as such, but rather a grammatical function. These must be annoying for translators and make learning languages a little bit harder/more interesting, but we can learn what the nuances are.
Then there's the kind that seem somehow exotic because they refer to some concept that we hadn't thought about before. These have a great appeal on the internet. I suspect this is because they tend to refer to highly emotional states of mind. Nostalgia would be a good example of this in English, and saudade in Portuguese. They are often claimed to say something about the temperament of the nation that uses that word, so Portuguese or Brazilians are typically melancholic or nostalgic. We know the fallacy of attributing a characteristic to a whole nation, but nevertheless we like to do it because it helps us to label people.
Gezellig is said on Wikipedia to 'encompass the heart of Dutch culture', so it's a good example of one of these 'untranslatable words'. Wiktionary says it means 'companionable, having company with a pleasant, friendly atmosphere, cosy atmosphere or an upbeat feeling about the surroundings'.
It also says it comes from gezel, which means 'companion'. So much for my etymological analysis.