Gustakhi is something like insolence, it means being disrespectful to someone you should be respectful to. To give you a better idea, I'd give you an example. Disobeying someone you are supposed to obey is probably the most common type (and hence the best example) of 'gustakhi.' In the era of Kings, doing anything disrespectful is a 'Gustakhi.' One thing that is rarely told about the word, but always understood, is that supposedly you cannot do a 'gustakhi' against someone who is below you in standard and doesn't deserve your respect.
The person who does this 'gustakhi' is a 'gustakh.' Roughly, you can say a Gustakh is someone who refuses to obey.
NDTV's famous program is also named Gustakhi Maaf as they make fun of powerful politicians, and hence the name which means 'the insolence be pardoned.'