Payoff is the notional times the difference between realised variance and the strike variance. Because it is linear in variance and not in volatility, the payoff is convex in volatility: a doubling of volatility quadruples variance, which makes the short side's losses grow disproportionately.
The instrument exists because trading volatility with options requires constant delta hedging to remove directional exposure. A variance swap packages that hedged position, which is why its strike sits close to a weighted average of option implied-volatility across strikes.
Short variance positions carry severe tail risk and have caused notable losses in volatility spikes. Capped variants exist that limit the payoff at a multiple of the strike, and should be preferred by anyone selling. See volatility-arbitrage and dispersion-trade.
Related: volatility-arbitrage, dispersion-trade, implied-volatility, swaption, tail-risk, straddle