A trading edge in the financial markets can be described as a set of conditions that when present, give a higher probability of a trade working than not working.
An example of an edge could simply be identifying when the market is trending, in which case you base your trades on the direction of the trend. If you take trades in the direction of the trend, you have a higher probability of producing profitable trades.
Despite having an edge, there will be losing trades as well as winning trades. Trading in the direction of a trend does not guarantee a winning trade, merely a higher probability of a trade working out. The first trade that you take in the direction of the trend could be a losing one. However, taking a series of trades in the direction of the trend is likely to result in trades that win.
Also referred to as just an 'Edge'