What economics aggregate(s) could suggest an imminent change in exchange rates? I have read articles about the Swiss Franc breaking its peg with the dollar and I would like to understand what indicators people look at to determine whether a currency break/depegging is imminent. More which of these useful economic aggregates are most important in determining a currency peg break?
If they expected the peg to break then it is clear that the franc would gain in value. Since the currency has been held artifically cheap by the central bank, i.e. would have gained value if the central bank had not intervened, then the moment the central bank stops intervening (abandons the peg) the currency will appreciate.

Why would it have gone up otherwise, i.e. what are the factors driving exchange rates? We call these "fundamentals". Basically exchange rates are determined by supply and demand for a currency, just like for anything else. So basically anything influencing supply and demand for currencies would be cause for a change in exchange rates. Further expectations of changes in fundamentals cause them as well. These include the trade balance (typically governs the long run behavior of exchange rates in reality) and the difference between domestic and foreign interest rates (typically govern the short run behavior in reality).

Now one might ask, why did they expect the peg to be abandoned? That depends on the specifics about Switzerland. I'm not an expert there, so I'm sorry if I cannot give a very concrete answer. However pegs are typically unstable and usually abandoned eventually. This is because the longer the central bank keeps a currency at the "wrong" price, the more pressure from the market there is to correct it which means the central bank must fight harder and harder to keep it and eventually gives up or decides its not worth it anymore.