I think the concept of edge comes from probability theory. Each bet with a predifined reward to risk ratio has a mathematical edge if the implied probability of the bet is lower than the real probability for the outcome. If you bet on flipping coins with a reward bigger than the risk, you have a mathematical edge, because the probability of a win is 50%. If you divide 1 to the reward to risk ratio + 1, you get the implied probability for that bet. If someone offers you 1.1$ profit for rach 1$ risked at flipping coins, the implied probability for that is 1/(1+1.1)=0.47619 -> 47.618%. If you bet on that you have a mathematical edge as long as you don't over bet (according to the kelly criterion formula) and the law of large numbers is saying that you will make money in the long run. Casinos have a mathematical edge because they offer bets with a higher implied probability than the real one (think of the 0 and double 0 at roulette). When talking about mathematical edge it is crucial to factor in the percentage of capital risked. If the risk is higher than what kelly criterion formula recommends, those bets lead to losses in the long run according to the law of large numbers, regardless of the apparent edge.
Edge is a trade setup you discover (any imaginable trading style) that when you take the risk of loss each trade the profits will surpass the losses by a greater amount the larger the sample size. Negative edge sounds like not letting the trade play out and succumbing to noise induced fear. You could see a monster order print against your trade and get out only to find it was absorbed and continue in your direction.
Edge is different for everyone, when young trader they often think is terms has something to do with entries or methods themselves, when you down the block a good deal it might change to nothing but risk management. If you get one's rules of managing trade where negative expectancy to be under 10 or even 5%, one can use more capital into the signals. And if you going to copy from other people's articles, use quotations and where it came otherwise it is called plagiarizing.
An edge is when your P&L is in the green. When its in the red the market has your supposed edge covered.
As Handle alluded, the edge in trading is the ability to utilize Prudent Risk Management when trading. There is no other edge--PERIOD
Folks, traders only have one item available that can set their performance apart from other traders results, and that is the ability to manage risk. Most traders are unable to do this even though they can look at charts many times and come up with direction.