Omega divides the area of the return distribution above a chosen threshold by the area below it. At a zero threshold, a strategy whose gains sum to 180 units and whose losses sum to 100 has an omega of 1.8.
Its appeal is that it uses every moment of the distribution - mean, variance, skew, kurtosis - rather than just the first two, so it does not assume normality. It also changes with the threshold you pick, which is a feature: plotting omega across thresholds shows how a strategy performs for investors with different requirements, and two strategies can swap ranking as the bar rises.
In practice it is close to a generalised profit-factor on returns rather than trades, and it inherits the same limitation as every historical measure: rare large losses that have not occurred yet contribute nothing to the denominator.
Related: profit-factor, gain-to-pain-ratio, return-skew, sortino-ratio