"기가 막히게 맛있어!"
"This is unbelievably delicious", "It was so delicious that I became dumbfounded"
For more vocabulary including '맛있게 드셨어요? (Did you enjoy the food?), please visit http://www.laughingbeans.com/learn/class/170
"기가막히다": dumbfounded, taken aback, pleasantly surprised.
'기가막히다' is very useful phrase and has various forms.
'기' itself means spirit (정신) and '막히다' means 'blocked', 'clogged'. So 기가 막히다 means your spirit is blocked. So it means you are at a loss.
It has both positive and negative meanings. (In this clip, apparently used as a positive meaning) You would feel 기가막히다 when you see or experience something extraordinary (either good or bad)
In this clip, Sam says 기가 막히"게" 맛있어. By replacing '다' in 기가막히다 with '게', the phrase (기가막히게) becomes a adjective which modifies 맛있어.
[ Examples ]
1) 남자친구가 바람핀걸 알게 되었을 때 너무 기가 막혀서 말이 안나왔어.-> I was so dumbfounded that I became speechless when I found out that my boyfriend cheated on me.
2) 제주도 한라산 경치가 정말 기(가) 막히게 아름다웠어.The scenery of Mt.Halla of Jeju Island was unbelievably beautiful.
You can say '기막히게' instead of 기가 막히게.
You can just use this phrase only when you experience something negative. For example, if a passer-by hits you by mistake and just has gone without saying 'sorry', then you can say '기가막혀'.