The House Edge is a statistical advantage that the casino has over a player in online casino games. The house edge varies from game to game and depends on bets and rules of the game. It is calculated based on odds - the probabilities of winning and losing. Those are closely related to bets and the way online casino games manage bets. Generally speaking, the house edge is difference between the true odds of winning and the amount you get when you win.
Let's take a classic example: a coin flipping game. A coin has two sides - heads and tails - each having equal probability of 50%. As we said in our Guide to Bets, a bet is a price you pay for the right to participate and try to win under the risk of winning nothing and losing the bet as opposed to winning something and keeping the bet. An even odds bet would be a bet under which you win exactly as much as you risk: if you bet $1 on tails and tails plays out, you receive back your bet and your win - $1. Otherwise you lose your bet. However if the conditions of the game declared that your win should be 95 cents on each risked dollar we'd say that in an otherwise equal (50% vs 50%) game the house has a 5% advantage. If you play 100 games against the house under these conditions the following will theoretically (!) happen:
Of course in real online casino games probabilities are absolutely different and so are the betting schemes, but house edge can still be calculated predictably for most of online casino games. The calculations above do not mean that you will keep losing money in online casinos; the statistics only works on very large number of casino games and players meaning that the players' money gets reallocated and that's where your luck comes in. Look at it this way: when you see someone losing $10 on a bet with 5% house edge it is likely that of those ten dollars the online casino will receive fifty cents and someone else would win $9.95. Remember that the house edge is a statistical variable that can not and should not be used to predict realistic wins and losses of a single player in an online casino over a period of time.
Generally speaking, the online casino advantages are very low. The point of casino game design is to keep precise balance of fairness on both sides and prevent either side from having any possibility to facilitate abuse. The probabilities are adjusted so that the online casino will be always profitable while letting some players to walk away with huge wins.