calorie and exercise deficits

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Hi,
I'm new on here and have got my first hurdle.
I've been doing this for two weeks now. The 1st week I lost 2 pounds, this week i've been struggling to loose even one.
Last night I read a few posts on here and it said you have to eat your exercise calories.
So if i'm on a 1200 a day allowance and say I burn 500 calories, do I have to eat most of them to loose weight..have I got that right??
I need to feed the fat to get rid of the fat?
I'm really quite confused and really enjoying my new found exercise regime. Some days I'm burning 700+ so also want to see some results!
If anyone has any advice or tips for me please share them x

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