In trading, the handle has two meanings. In most markets, it means the whole numbers involved in a price quote, without the decimals included. In forex, the handle refers to that part of the quote that appears in both numbers of the spread.
Both offer a faster way of referring to the price of an asset at a particular point in time. If a stock is trading at $46.24, its handle is just $46. If a currency pair can be bought for 1.6456 and sold for 1.6400, then its handle is 1.64.