What does it mean when someone says “2 trillion wiped off markets”? After a major global event, sometimes the markets move and headlines are written saying something like “2 trillion wiped off markets”. But what does this actually mean? Does it mean the aggregate value of companies on the exchanges has been reduced?

After Brexit similar headlines were generated, has the market recovered its value yet?
That's connected to the way currency or prices fluctuate, particularly in the stock exchange. It comes from the approach that value (e.g. of a firm) equals the sum of all the stocks at current price. That's often called the "Market Cap(italization)".

Think of a firm A with 10.000 stocks. If from one day to the other the stock of company A goes from 100€ to 50€, then its market capitalization/market value goes from 1M€ (=10.000 stocks * 100€) to 500k€. In this conditions you could say that half a milion was wiped off the market or from this company.

That answers directly to your question, but keep in mind that there are many other ways of calculating the value of a firm.