Definition
Sharpe = (return minus risk-free rate) / standard deviation of returns.
Return per unit of risk. It makes strategies with different leverage comparable, which is why it is the industry default.
Time scaling
For independent returns, mean scales with t and standard deviation with sqrt(t), so:
Sharpe scales with sqrt(t).
A daily Sharpe of 0.1 annualises to 0.1 times sqrt(252) ≈ 1.6.
This is the square-root-of-time law again, and interviewers ask you to annualise on the spot.
The assumption of independence matters: with positive autocorrelation the scaling overstates the annual Sharpe, which is one way reported figures get inflated.
How long to measure it
The important practical result. The standard error of a Sharpe estimate is approximately 1 / sqrt(number of years).
To distinguish a Sharpe of 1 from zero at conventional significance you need roughly 4 years of data. To distinguish a Sharpe of 1 from 0.5, considerably longer.
This is why claims about strategy quality from short track records deserve scepticism, and it is a favourite question: "A manager has a Sharpe of 2 over 6 months. Impressed?" Not much - the standard error over half a year is about 1.4.
Limitations
Penalises upside volatility. A strategy that occasionally makes very large gains is punished for it. The Sortino ratio uses downside deviation instead.
Ignores tail shape. Selling far out-of-the-money options produces a superb Sharpe for years, followed by a catastrophic loss. Sharpe cannot see the shape of that risk at all, which is its most dangerous blind spot.
Assumes volatility captures risk. For non-normal return distributions, it does not.
Manipulable. Smoothed or illiquid marks understate volatility and inflate Sharpe, which is a known issue in some fund reporting.
In the interview
Being able to annualise quickly, state the estimation-error result, and name the tail-risk blind spot is a complete answer.
Practise in statistics.