Atrangi is not a word generally found in Hindi dictionaries, but it's almost a well-known word now, with a pretty well-defined Meaning. In Hindi speaking regions, the word seems to be coming from the parts 'at', or rather 'ati', which means a lot, or too much, and 'rangi', which means colourful. So something that is too colourful, not just literally but figuratively, is called Atrangi.

There is a Hindi word atiranjit (अतिरंजित) which has the same meaning, and atrangi can be considered a tadbhava for the word.

As for the film Atrangi Re, the film's makers say that atrangi means funnily weird, which is a good way to explain what we called 'too colourful.'