Heather did a pretty good job of explaining the “constant” basics. It’s pretty convoluted in the LOSTiverse with the time traveling and warping and whatnot. 😆 In a sense, Emma does have two timeframes she’s living in – her pre-fairytale life, and her fairytale life, and she has to reconcile the two, and Neal is a part of both.
Daniel Faraday explains that when a consciousness travels back and forth through time, it needs a constant to latch on to. A constant is an object or person that exists in both periods of time, that the traveler deeply cares about and could recognize. If a constant is not found, the oscillations between different times will become more frequent and chaotic until the individual dies from what appears to be a severe brain aneurysm.
http://lostpedia.wikia.com/wiki/Constant
Brief summary of the plot of the ep titled The Constant: http://en.wikipedia.org/wiki/The_Constant