Definition
Edge is your expected profit per trade. Buy at 99 something genuinely worth 100 and your edge is 1.
It is expected value applied to a position, and interviewers use the words nearly interchangeably.
Positive EV is not enough
Three reasons a positive-EV trade can still be wrong.
Size. An edge of 1 on a position that can lose 10,000 and would ruin you is not worth taking, however positive. See Kelly and gambler's ruin - bankroll constraints bind.
Estimation error. Your edge is an estimate. If you think it is 1 but your uncertainty around that is plus or minus 3, you may well be trading a negative-EV position with confidence. Edges computed from small samples are especially suspect.
Adverse selection. The edge you calculate assumes you get filled at random. You do not - see adverse selection. Realised edge is systematically worse than quoted edge.
Edge per unit of risk
The useful comparison between opportunities is not raw edge but edge relative to the risk taken. A trade with edge 1 and standard deviation 2 is far better than one with edge 3 and standard deviation 30, because you can do the first one many times.
This is the intuition behind the Sharpe ratio and behind why market makers prefer thousands of small edges to a few large bets.
The law of large numbers is the business model
A market maker capturing a small edge thousands of times a day has a distribution of daily P&L concentrated tightly around a positive number. The same total edge taken as one large bet has enormous variance.
That is the entire structural argument for market making as a business, and it is a good thing to be able to articulate.
In the interview
When offered a bet, do not stop at "positive EV, I take it". Say what your edge is, what your risk is, and what size you would do. Candidates who compute EV correctly and then accept an unbounded-downside bet at full size are demonstrating exactly the failure mode a desk cannot afford.
Practise in expected value and the take the bet game.