1. It was originally a slang term used in Ireland to [mean either] a) "to steal" or b) "to throw".
2. It's also used as a pretty mild swear word in Ireland.
It's used a) to express that [you're pissed] off or b) to describe somebody who pissed you off.
It's not related to the word 'Fuck', and doesn't have any sexual undertones, so is acceptable for polite company.
3. The characters in the sit-com [Father Ted] made the use of 'Feck' more popular outside of Ireland, most noticeably in the United Kingdom.
Unlike what a lot of people think, the scriptwriters did NOT invent 'feck' to get past censors who didn't allow the word 'fuck'. In fact, 'feck' was used as a mild swear word LONG before Father Ted made it famous!